Let Y be a Poisson random variable with mean λ = 2. (a) Find P(Y ≥ 2). (b) Find P(Y ≥ 4|Y ≥ 2).

Y1=X1-3*X2+X3

Z is the present-value random variable for a whole life insurance of b payable at the moment of death of (x). You are given: (i) (ii) 8 = 0.05 (iii) The net single premium for this insurance is equal to Var(Z). Calculate b. x+t = 0.01 t≥0 (A) 1.36 (B) 1.68 (C) 2.00 (D) 2.32 (E) 2.64

C1. Let X be a continuous random variable with PDF f(x) = (2-x) ² for -1 1)? (c) Calculate the expectation of X. (d) Calculate the variance of X.

Let X be a random variable with mean E[X] = 20 and variance Var(X) = 3. Define Y = 3 – 6X. Calculate the mean and variance of Y.

Let X be a random variable with distributionfunction mX(x) defined by mX(−1) = 1/5, mX(0) = 1/5, mX(1) = 2/5, mX(2) = 1/5 (a) Let Y be the random variable defined by the equation Y = X + 3. Find the distribution function mY (y) of Y .(b) Let Z be the random variable defined by the equation Z = X2. Find the distribution function mZ(z) of Z.

Let the random variable X be defined on the support set (1,2) with pdf fX(x) = (4/15)x3, Find the variance of X.

Let X1, . . . , Xn be iid from Exp(β). Find the distribution of the sample maximum Y = X(n). Is this an exponential distribution?  (This question was rejected this morning. I did double check and there is no missing info with this question.)

In a poisson distribution P(X=0) = P(X=2).Find the variance V(X) of X.

Let Y be a continuous random variable with √ ½ (2 f(y) = = Find the mean (u) and variance (o²) of Y. (2−y), 0≤ y ≤ 2 elsewhere.