If Yis a discrete random variable that assigns positive probabilities to only the positive integers, show that E(Y) = P(Y ≥ k). Σ i=1

Q: f x is a binomial random variable, find p (x) for n = 6, x = 3, p = 0.5.

A: Solution: Let X has binomial random variable with parameter n= 6 and p= 0.3 X~B(n=6,p=0.5) The…

Q: Let X, Y are random variables (r.v.) and a, b, c, d are values. Complete the formulas using the…

A: Step 1: Step 2: Step 3: Step 4:

Q: E(Y) –> P(Y > n).

A:

Q: (a) f(x) = c(x² + 6), for x = 0, 1, 2, 3 5 3 - (:) ( 2² X (b) f(x) = c 3-x for x = 0, 1, 2

A: It is given that a probability distribution of the discrete random variable X.

Q: Assume I observe 3 data points x1, x2, and x3 drawn independently from the same unknown probability.…

A: From given data we have : Prx1|M=0.5,Prx2|M=0.1,Prx3|M=0.2.

Q: Suppose that the random variables X and Y are independent with Var(X)=8 and Var(Y)=6. Calculate…

A: Given Data: Var(X)=8 Var(Y)=6

Q: Let X and Y be independent, taking on {1,2,3,4,5} with equal probabilities.  E((X+Y)2)=?

A: We have given that X and Y be independent random variables.   The distribution of X is: P( X=x ) =…

Q: Let X be a geometric random variable with p= 1/3. Compute E(X³).

A: Let X be a geometric random variable with p=1/3.

Q: Suppose that X is a geometric random variable with parameter π. Show that P(X = n+k|X > n) = P(X =…

A:

Q: suppose that X is a random variable with probability distribution.P(X=k)= 0.02k,where k takes the…

A: Given: P(X=k) = 0.02k k = 8,12,10,20 Here takes the value 8,12,10,20

Q: f X1 and X2 are independent exponential random variables with respective parameters λ1 and λ2, find…

A: Given:    X1, X2 are two independent exponential random variables with respective parameters λ1 and…

Q: Assume that a researcher randomly Probabilities of Girls selects 14 newborn babies and counts…

A:

Q: 2. Let X be a binomial random variable with E(X) = 30 and Var(X) = 21. Find the parameters n and p…

A: Given that  X~Bin(n,p) Here n and p are parameter.

Q: Let Z be a discrete random variable withE(Z)=0. Does it necessarily follow that E(Z3)=0? If yes,…

A: Solution

Q: Let X be a discrete random variable with P(X = -1) = .3, P(X = 1) = .45, P(X = 2) = .15 and P(X = 6)…

A: The following information has been given: We have given that X is a discrete random variable. P(X =…

Q: Let X be a Poisson random variable with E(X) = 3. Find P(2 < x < 4).

A: When X~ Pois(λ) P(X=x)=e-λ λx/x!  ; X=0,1,2,3,.. result: r!=r(r-1)(r-2)..3x2x1

Q: (a) find f(x) (b) Calculate E[X] and V[X]

A: Answer:- Total children = 12 boys+4 girls=16 So, the rank of second boy i.e x can be 2 or 3 or 4 or…

Q: -{* S a2-a x = 0, 1, 2, .. Px(x) = { ? otherwise a) Find the constant a b) The base station can…

A: "Since you have posted a question with multiple subparts, we will solve first 3 sub-parts for you.…