Q1. Given that (x, y) = (3x+2y)/5k if x = 1,5 and y = -2,3, is a joint probability distribution function for the random variables X and Y. a. Find: The value of K b. Find: The marginal function of x c. Find: The marginal function of y.

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A: Solution:         ut   x1    x2 , x3    iid ~N(u=0, α2=1)         ut  Y1 = x1 +δ x3 & y2= x2+δx3…

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Q: 3. Let X denote the number of times a machine will malfunction, 1,2 or 3 times on any given day. Let…

A: The marginal distribution of X: X 1 2 3 PX=xi 0.05+0.05+0.1=0.2 0.05+0.1+0.35=0.5 0+0.2+0.1=0.3…

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Q: I. Let X be the number of courses that thirty part-time students were taking this term. The…

A: Given data is  Number of Courses (x) P(x=x) 1 5/10 2 10/30 3 7/30 4 4/30 5 2/30 6…

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A: The cumulative distribution function of x is given as:

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Q: b. Find E[X(X – 1)] for Poisson random variable. Use the result to find the variance of X.

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Q: Question 2 et Y~ B(n = 2,p=0.5). 1. Construct the probability distribution table for Y. k P(Y = k) =…

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A: f(x,y)=c  ,  for x=-2,0,2  ; y=-2 , 3

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A: P(X=x)=p(1−p)x−1;x=1,2,3,...

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A: given data  exponential distribution λ = 3.3 P(x does not fall in interval 0.3 to 0.4) = ?

Q: Y 1 2 4 8. 16 |P(y) 0.05 0.10 0.35 0.40 0.10 Construct the cumulative distribution function.

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A: The provided information is as follows:The probability mass function is given as…

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A: Given: X is a random variable. E(X)=6.2 E(X2)=62.5

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Q: Let x2-z,2+ z22. Za is chi-square distribution random variable, where df = 54. What is the standard…

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Q: .Given that (x, y) = (x+2y)/k if x = -2,1 and y = 3,4, is a joint probability distribution function…

A: Note: Hi! Thank you for the question, As per the honor code, we are allowed to answer three…

Q: The marginal distributions of two random variables X and Y, together with some values of their joint…

A: Given  P(X=0)=0.5, P(X=1)=0.3, P(X=2)=0.2 P(Y=1)=0.5, P(Y=3)=0.5  Result: If X and Y are independent…

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Q: A probability distribution function is modeled by the following X-Y cartesian graph: 15 kT 长 6 7 12…

A: Solution Given

Q: Suppose that X is a Normal random variable with E(X) = 1 and Var (X) = 1. Define Y =2X + 1. Find P(0…

A: Consider, EY=E2X+1=2EX+1∵EaX+b=aEX+b=2*1+1=3 VarY=Var2X+1=22*VarX∵VaraX+b=a2*VarX=4*1=4 SDY=VarY=4=2

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A: Given function is f(x)=116(2x+1)   X=0,1,2,3

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Q: If X and Y have the joint probability distributionf(x, y) = 14 for x = −3 and y = −5, x = −1 andy =…

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