Two discrete random variables have a joint PMF as described in the following table. PM (m, n) m = 1 2 m = 3 n=1 1/5 7/45 1/9 n = 2 8/45 4/45 2/45 n = 3 2/15 1/15 1/45 (a) Find the marginal PDFs, P(m) and Py(n). Р (b) Find Pr(N=1|M= 2). (c) Find Pr(MEN). (d) Find Pr(M>N).
Answers
a. P(1) = 0.3556, P(2) = 0.3111, P(3) = 0.0444; Py(1) = 0.5333, Py(2) = 0.4444, Py(3) = 0.1222 b. P(N = 1 | M = 2) ≈ 0.2574 c.P(M = 2, N = 3) ≈ 0.038 d. Pr(M>N) = 0.5333.
a. The marginal probability function of m is given by P(m) = Σn P(m, n) and that of n is given by P(n) = Σm P(m, n).
Thus, the marginal PDFs are: P(1) = 1/5 + 8/45 + 2/15 = 0.3556 P(2) = 7/45 + 4/45 + 1/15 = 0.3111
P(3) = 1/9 + 2/45 + 1/45 = 0.0444 P(1) + P(2) + P(3) = 1 Py(1) = 1/5 + 7/45 + 2/15 = 0.5333
Py(2) = 8/45 + 4/45 + 1/15 = 0.4444 Py(3) = 2/15 + 1/15 + 1/45 = 0.1222 Py(1) + Py(2) + Py(3) = 1.
b. We need to find P(N = 1 | M = 2).
From the joint probability distribution table, we can see that P(N = 1, M = 2) = 8/45. P(M = 2) = 0.3111.
Using the conditional probability formula, P(N = 1 | M = 2) = P(N = 1, M = 2)/P(M = 2) = 8/45 ÷ 0.3111 ≈ 0.2574
c. We need to find the probability that M = E and N = N.
Since the two random variables are independent, we can simply multiply their probabilities: P(M = E, N = N) = P(M = E) × P(N = N).
The probability distribution of M is given by: M=1 with probability 0.3556 M=2 with probability 0.3111 M=3 with probability 0.0444
The probability distribution of N is given by: N=1 with probability 0.5333 N=2 with probability 0.4444 N=3 with probability 0.1222
Therefore, P(M = 2, N = 3) = P(M = 2) × P(N = 3) = 0.3111 × 0.1222 ≈ 0.038
d. We need to find P(M > N).
There are three possible pairs of values for (M, N) such that M > N: (M = 2, N = 1), (M = 3, N = 1), and (M = 3, N = 2).
The probabilities of these pairs of values are: P(M = 2, N = 1) = 1/5 P(M = 3, N = 1) = 1/9 P(M = 3, N = 2) = 1/15
Therefore, P(M > N) = P(M = 2, N = 1) + P(M = 3, N = 1) + P(M = 3, N = 2) = 1/5 + 1/9 + 1/15 = 0.5333.
Answer: a. P(1) = 0.3556, P(2) = 0.3111, P(3) = 0.0444; Py(1) = 0.5333, Py(2) = 0.4444, Py(3) = 0.1222 b. 0.2574 c. 0.038 d. 0.5333
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Related Questions
x/12-5>-2 please help
Answers
Answer:
Your math problem
1
2
−
5
>
−
2
can i get brainliest plz :)
2x-2y= 14 standard to slope and intercept form
Answers
2x - 2y = 14
-2y = 14-2x
y= -7 + x
y = x - 7
g In the absence of voltage-gated K+ channels (delayed rectifier K+ channels), why would the closure of voltage-gated sodium channels allow the membrane potential of a neuron return to its original resting potential? a. Sodium would continue to leak into the neuron after the closing of the voltage-gated Na+ channels b. The sodium-potassium-ATP pump would lower intracellular K+ concentrations c. Sodium would leak out of the neuron anyway d. Neuronal membrane are far more permeable to potassium than sodium when the membrane is at rest. As a result, the resting potential is close to the equilibrium potential of potassium
Answers
The closure of voltage-gated sodium channels allow the membrane potential of a neuron return to its original resting potential d) d. Neuronal membranes are far more permeable to potassium than sodium when the membrane is at rest. As a result, the resting potential is close to the equilibrium potential of potassium.
The correct answer is d. Neuronal membranes are far more permeable to potassium than sodium when the membrane is at rest. As a result, the resting potential is close to the equilibrium potential of potassium.
The resting potential of a neuron is primarily determined by the balance of ion concentrations and the permeability of the neuronal membrane to different ions. At rest, the membrane is highly permeable to potassium ions (K+), which allows potassium to freely move in and out of the cell. This permeability is mainly due to the presence of leak channels for potassium.
In the absence of voltage-gated potassium channels, the closure of voltage-gated sodium channels would still allow sodium ions (Na+) to leak into the neuron, as stated in option a. However, the key point is that the leak of sodium alone is not sufficient to bring the membrane potential back to its original resting potential.
The primary factor in restoring the resting potential is the high permeability of the neuronal membrane to potassium ions. As the membrane potential depolarizes during an action potential, voltage-gated sodium channels open, allowing sodium ions to rush into the cell and contribute to depolarization. However, once the action potential reaches its peak and the voltage-gated sodium channels close, the high permeability of the membrane to potassium ions allows potassium to quickly move out of the cell, repolarizing the membrane and restoring the resting potential.
Option d correctly explains that the resting potential is close to the equilibrium potential of potassium because of the high permeability of the membrane to potassium ions. This permeability allows potassium to flow out of the cell, counteracting the depolarizing effects of sodium influx and bringing the membrane potential back to its resting state.
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) Complete the equations.
-3.
?
= 21
21 : (-3)
?
please help
Answers
Answer:
-7 for both of them
Step-by-step explanation:
How much is car insurance for a 18-year-old per month.
Answers
Car insurance for an 18-year-old typically ranges from $200 to $400 per month.
The cost of car insurance for an 18-year-old can vary significantly depending on various factors. Young drivers, especially those with limited driving experience, are generally considered higher risk by insurance companies, which leads to higher premiums. Insurance providers take into account factors such as the driver's age, gender, location, type of vehicle, driving record, and credit history. Additionally, factors like the level of coverage and deductibles chosen, as well as discounts available, can also impact the cost. It's important for young drivers to shop around and compare quotes from different insurance companies to find the best coverage options at the most affordable rates. Additionally, taking driver's education courses and maintaining a clean driving record can help in reducing insurance costs over time.
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What is the average monthly cost of car insurance for an 18-year-old?
I only have 3 more left pls help I am giving brainly throughout these questions
Answers
Step-by-step is this the answer you wanted thanks for correcting me
Answer:
Step-by-step explanation:
\(y = \frac{2}{3}x - 4\\\\when \ y = 0, \ x = \frac{4 \times 3}{2} = 6\\\\When \ x = 0 , \ y = - 4\)
A family went on Vacation and used 5.4 gallons of gasoline to travel 150 miles how many total gallons of gasoline will be to travel 350 miles
Answers
The volume of water in a rectangular, in-ground, swimming pool is given by V(x ) =x3 + 11x2 + 24x where V (x) is the volume in cubic feet when the water is x ft high
What is the dimension of the base of the pool? (a) x + 3 and x + 8 (b) x + 4 and x + 7 (c) x + 4 and x + 8(d) x + 3 and x + 7 What is the volume of the pool when x = 3 ft?
(a) 298 ft3 (b) 148 ft3 (c) 268 ft3 (d) 198 ft3
If the volume is 100 ft3 of water, what is the height x ? (a) 2 ft (b) 3 ft (c) 4 ft (d) 5 ft
If the maximum capacity of the pool is 520 ft3 what is the maximum depth? (a) 2 ft (b) 3 ft (c) 4 ft (d) 5 ft
Answers
1) The dimension of the base of the pool is; (x + 3) and (x + 8)
2) The volume of the pool when x = 3 ft is; 198 ft³
3) If the volume is 100 ft³ of water, the height x is; 2 ft
4) If the maximum capacity of the pool is 520 ft³, the maximum depth is; 5 ft
How to find the volume of a cuboid?We are given that the volume of water in a rectangular, in-ground, swimming pool is; V(x) = x³ + 11x² + 24x
where;
V(x) is the volume in cubic feet when the water is x ft high
1) V(x ) =x³ + 11x³ + 24x
V(x) is the volume in cubic feet when the water is x ft high
Factorizing the polynomial into its' factors gives;
V(x) = x(x² + 11x + 24)
V(x) = x(x + 8)(x + 3)
The water is x ft high and so the dimensions of the base of the pool are (x + 3) and (x + 8)
2) We want to find the volume of the pool when x = 3 ft. Thus;
V(3) = 3(3 + 8)(3 + 3)
V(3) = 3 (11)(6)
V(3) = 198 ft³
3) If the volume is 100 ft³ of water, the height x is calculated as;
x(x + 8)(x + 3) = 100
Solving for x gives us;
x = 2 ft
4) If maximum capacity of the pool is 520 ft³, then the maximum depth is;
x(x + 8)(x + 3) = 520
Solving for x gives us;
x = 5 ft
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Morgan won 7 blue ribbons and 4 red ribbons at her horse shows. What is the ratio of red ribbons to blue ribbons she won?
a. 4/11
b. 4/7
c. 7/11
d. 7/4
Answers
Assume you deposit $1,000 every three months at a 3 percent
annual rate, compounded quarterly. How
much will you have at the end of 5 years?
Answers
The future value of the deposits at the end of 5 years is approximately $6,138.74.
To calculate the future value of the deposits, we can use the formula for compound interest:
FV = P(1 + r/n)^(nt)
Where: FV is the future value
P is the principal amount (initial deposit)
r is the annual interest rate (3% in this case)
n is the number of times interest is compounded per year (quarterly in this case)
t is the number of years
In this case, the principal amount is $1,000, the annual interest rate is 3% (or 0.03), the number of times interest is compounded per year is 4 (quarterly), and the number of years is 5.
Plugging in these values into the formula, we get: FV = $1,000(1 + 0.03/4)^(4*5)
Calculating this, the future value of the deposits at the end of 5 years is approximately $6,138.74.
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The surface area of the side of the cylinder is given by the function f(r) = 6π r, where r is the radius. If g(r) = π r2 gives the area of the circular top, write a function for the surface area of the cylinder in terms of f and g.
Answers
Answer: the answer is 24
Which expression represents the sentence "five times a number, n"?
Answers
Answer:
5n
Step-by-step explanation:
:)
Answer:5n
Step-by-step explanation:
The index of refraction of the core of a typical fiber optic is ncore = 1.46; the cladding has nclad = 1.4. calculate the critical angles for the total internal reflection icrit and crit .
Answers
Critical angle for the total internal reflection icrit, β = 78.28⁰
Critical angle for the total internal reflection crit, α = 17,22⁰
We have the refractive index of core, \(n_c_o_r_e\) = 1.46
We have the refractive index of clad , \(n_c_l_a_d\) = 1.4
Critical angle can be defined as the incidence angle which results in the refraction angle being equal to at that angle of incidence.
For Total Internal Reflection to occur, the incidence angle must be greater than the critical angle.
We know that the critical angle, θ is given by:
sinθ = \(\frac{n_c_l_a_d}{n_c_o_r_e}\)
sinθ = \(\frac{1.4}{1.46}\)
sinθ = 0.959 = sin⁻¹(0.979) = 78.28⁰
β = θ = 78.28⁰
Now, for α:
\(\frac{sin(90-\alpha )}{sin\alpha } = \frac{1}{n_c_o_r_e}\)
sinα = sin(90⁰-78.28⁰) × 1.46
sinα = sin(11.72⁰) × 1.46
α = sin⁻¹(0.296)
α = 17,22⁰
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Critical angle for total internal reflection icrit β = 78.28⁰
Critical angle for total internal reflection crit, α = 17.22⁰
The critical angle can be defined as the angle of incidence at which the angles of refraction are equal to angle of incidence.
The angle of incidence must be greater than the critical angle for total internal reflection to occur.
The refractive index of the core is ncore = 1.46.
The refractive index of clad is nclad = 1.4.
We know that the critical angle, θ is given by:
sinθ = nclad/ ncore
sinθ = 1.4/1.46
sinθ = 0.959
sin⁻¹(0.979) = 78.28⁰
β = θ = 78.28⁰
Now, for α:
sin(90- α) / sin α = 1 / ncore
sinα = sin(90⁰-78.28⁰) × 1.46
sinα = sin(11.72⁰) × 1.46
α = sin⁻¹(0.296)
α = 17.22⁰
Critical angle for icrit β = 78.28⁰
Critical angle for crit α = 17.22⁰
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5. Highlight only the TRUE STATEMENTS below ? (Hint: pick 2!)
All rectangles are quadrilaterals.
All quadrilaterals are rectangles.
All quadrilaterals are parallelograms.
4+ All quadrilaterals are squares.
All quadrilaterals are polygons with two pairs of parallel sides.
All quadrilaterals are polygons with four sides.
All quadrilaterals are polygons with at least one pair of parallel sides.
All quadrilaterals are polygons with four sides and at least one pair of parallel sides.
Answers
Answer:statement one and six
Step-by-step explanation:
-[-/7.14 Points] DETAILS LARPCALC11 6.4.036. Find the angle (in radians) between the vectors. (Round your answer to two decimal places.) u = 4i - 6j v = 5i + 4j 0 =
4. [-/7.14 Points] DETAILS LARPCAL
Answers
The angle (in radians) between vectors u and v is approximately 1.66 radians, rounded to two decimal places.
To find the angle between two vectors, we can use the dot product formula and the magnitudes of the vectors. Let's calculate the angle between vectors u and v:
Given:
u = 4i - 6j
v = 5i + 4j
Step 1: Calculate the dot product of u and v.
The dot product of two vectors u and v is given by:
u · v = |u| |v| cosθ
where |u| and |v| are the magnitudes of vectors u and v, respectively, and θ is the angle between them.
To calculate the dot product, we multiply the corresponding components of u and v and sum them:
u · v = (4 * 5) + (-6 * 4) = 20 - 24 = -4
Step 2: Calculate the magnitudes of vectors u and v.
The magnitude of a vector is given by:
|u| = √(u₁² + u₂²)
For vector u:
|u| = √((4)² + (-6)²) = √(16 + 36) = √52 ≈ 7.21
For vector v:
|v| = √((5)² + (4)²) = √(25 + 16) = √41 ≈ 6.40
Step 3: Calculate the angle θ.
Using the dot product formula mentioned earlier, we have:
-4 = (7.21)(6.40)cosθ
Solving for cosθ:
cosθ = -4 / (7.21 * 6.40) ≈ -0.086
To find θ, we can take the inverse cosine (arccos) of cosθ:
θ ≈ arccos(-0.086) ≈ 1.66 radians
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um pls help this question is very saddening
Answers
Answer: there is 2 small cups for icecream and 75 mediam ice cream bowls
Step-by-step explanation:
2 x 75 = 150
Can someone please help me and explain how to do it
Answers
Answer:
127
Step-by-step explanation:
so h(g(-5)) means that solve the function in a specific way. This means that solve for function h but the x is the answer to function g when x is -5. So first what u do is solve for g. Plug -5 in so u get -5-3 which is -8. Then u plug in -8 to function h. U have 2(-8)^2-1. Then u solve the square which is 64. Then u multiply that by 2 to get 128. Then u minus one to get ure final answer of 127. Hope this helps :D
Square WXYZ has coordinates W(-4, 5), X(-1, 5), Y(-1, 8), and Z(-4, 8). If the square is translated 1 unit left and 1 unit up, what are the coordinates of W'?
Answers
Answer:
it would be (-5,6) your welcome
What are the two points of a given slope?
Answers
Answer:
x1, y1
Step-by-step explanation:
Answer:
(x1,y1)
Step-by-step explanation:
i’ve already got 9 i believe, but could somebody please help with 10? it’s point slope form but i’m not understanding.
(15 points!)
Answers
Y=1/2x-2.5
The slope is 1/2, and y the intersect is around 2.5. I hope this helps!!
pls help, and explain. I will give brainliest
Answers
Answer:
Nicole should take 13 1/8 cups of snack mix.
Step-by-step explanation:
If a serving size is 7/8 and Nicole wants to take 15 serving sizes (15 7/8's), then we must multiply 7/8 by 15:
15 × 7/8
Write 15 over 1 (15 = 15/1) to make the calculations easier:
15/1 × 7/8
Multiply the numerators and denominators separately:
15 × 7 / 1 × 8
105 / 8
Instructions don't say you have to do this but I will convert this improper fraction into a mixed number:
105/8 = 13 1/8
-2y - 3y + 8 = 8 -5y - 12
solve this equation fast please
Answers
What we need to do is cancel both like terms on both sides of this equation which is
8=8 and you remove them.
Then you are left with -2y-3y=-5y-12
What you need to do is add -2y-3y because they are like terms
Now you have -5y
Then you put -5y=-5y-12
So you have to now cancel equal terms on both sides of this equation which were “-5y=-5y”, then you turn them into a 0
Now you are left with 0=-12
Therefore the statement is false for any value of y.
What is the approximate area of the figure below?
A. 27 square units
B. 29 square units
C. 30 square units
D. 36 square units
Answers
Answer:
C : 30 SQUARE UNITS
PQR is a right-angled triangle.
Work out the side of the angle marked x. Give your answer to 1 decimal
place. RP = 18 RQ = 15
Answers
The size of the angle marked x is 33.6°, using trigonometric ratios.
Trigonometric ratios are used in right triangles for the ratios of any two sides with respect to any acute angle of that triangle.
In the question, we are asked to find the size of the angle marked x.
In the given triangle, PQR, we can see that ∠Q = 90°.
By trigonometric ratios, we know that:
cos ∠R = QR/PR,
or, ∠R = cos ⁻¹ (QR/PR),
or, ∠R = cos ⁻¹ (15/18),
or, ∠R = cos ⁻¹ (5/6),
or, ∠R = cos ⁻¹ (cos 33.55730976°),
or, ∠R = 33.55730976°,
or, ∠R ≈ 33.6°.
Thus, the size of the angle marked x is 33.6°, using trigonometric ratios.
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if the class sizes in a school vary from 22 to 30, what is the range?
Answers
Answer:
8 im pretty sure
Step-by-step explanation:
First Flip
Second Flip
The probability of a biased coin
landing on heads is
Complete the tree diagram.
head
head
tail
head
tail
tail
Answers
Answer:
ANSWER:
IF RIGHT PLZ GVE ME BRAINLIEST
THANK U
Determine the equivalent system for the given system of equations: 5x 3y = 1 4x − 5y = 4
Answers
Answer: the equivalent system of equations is:
x = 17/37
y = -16/37
To determine the equivalent system for the given system of equations:
5x + 3y = 1
4x - 5y = 4
We can use the method of elimination. Here are the steps:
1. Multiply the first equation by 5 and the second equation by 3 to make the coefficients of x in both equations equal:
5(5x + 3y) = 5(1) --> 25x + 15y = 5
3(4x - 5y) = 3(4) --> 12x - 15y = 12
2. Add the resulting equations together to eliminate the variable y:
(25x + 15y) + (12x - 15y) = 5 + 12
25x + 12x + 15y - 15y = 17
37x = 17
3. Divide both sides of the equation by 37 to solve for x:
x = 17/37
4. Substitute the value of x back into one of the original equations to solve for y. Let's use the first equation:
5x + 3y = 1
5(17/37) + 3y = 1
85/37 + 3y = 1
3y = 37/37 - 85/37
3y = -48/37
y = -16/37
Therefore, the equivalent system of equations is:
x = 17/37
y = -16/37
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Solve for x
1) 6
2) 3
3) 4
4) 5
Answers
The value of the variable x in the circle using intersecting chords theorem is; 4
How to find the length of the chord?The intersecting chords theorem is defined as a statement in elementary geometry that describes a relation of the four line segments created by two intersecting chords within a circle. It states that the products of the lengths of the line segments on each chord are equal.
Thus, we can say that;
AB * BC = EB * BD
(4x + 2)(8) = 9 * 4x
32x + 16 = 36x
4x = 16
x = 16/4
x = 4
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17. What is the slope of a line parallel
to the line y = 3x - 4?
Answers
Answer:
The slope would be 3. All lines that are parallel have the same slope, and lines that are perpendicular have slopes that are negative reciprocals. The slopes are the same because slope represents rise/run on a graph, so for two lines to be parallel and never cross, the two lines must go in the same direc
Step-by-step explanation:
Answer: Y=3x
Step-by-step explanation: Have a great day.
Josiah plants vegetable seeds in rows. Each row has the same number of seeds in it. He plants more than one row of seeds. What could be the total number of seeds he plants?
Answers
The total number of seeds that Josiah would plant would be = nR×S
How to determine the total number of seeds that Josiah will plant?To determine the total number of seeds that Josiah will plant will be to add the seeds in the total number of rooms he planted.
Let each row be represented as = nR
Where n represents the number of rows planted by him.
Let the seed be represented as = S
The total number of seeds he planted = nR×S
Therefore, the total number of seeds that was planted Josiah would be = nR×S.
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