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- If a game gives payoffs of $10 and $100 with probabilities 0.9 and 0.1, respectively, then the expected value of this game is E=0.9+0.1= .4.20. How can I show that X is a Poisson random variable with parameter lambda, then E[Xn] =.... ? And after, using this result to compute E[X3]?Let X and Y be random variables with finite variance. Prove that |ρ(X, Y)| = 1 implies that there exist constants a, b and c such that aX + bY = c with probability 1.
- A continuous random variable X is defined by: Solve: 1. f(x) = (3+x)²/16 ; -3≤ x≤ -1 2. f(x) = (6 - 2x)²/16 ; -1≤x≤1 3. f(x) = (3 - x²)/16 ; -1≤x≤3How do you show that if X1, X2,...Xn are independent random variables having the same Bernoulli distribution with the parameter θ and Y =X1 + X2 + ... + Xn, then E(Y) = nθ and var(Y) = nθ(1-θ)26 - Since the continuous random variable X is normally distributed with parameters X~N(-3, 9) what is the probability of P(X=6)? a) 0.3413 B) 0 C) 0.3174 D) 0.8413 TO) one
- X is a continuous random variable taking values between 0 and 2. If F(1.5) = 0.70 and P(X<1) = 0.20, what is P (1 < X < 1.5)?Suppose a simple random sample of sizen=150 is obtained from a population whose size isN=10,000 and whose population proportion with a specified characteristic is p=0.2. (b) What is the probability of obtaining x=39 or more individuals with the characteristic? That is, what is P(p≥0.26)?If X1, X2, and X3 constitute a random sample of sizen = 3 from a Bernoulli population, show that Y =X1 + 2X2 + X3 is not a sufficient estimator of θ. (Hint:Consider special values of X1, X2, and X3.)
- If X1 and X2 are independent exponential random variables with respective parameters λ1 and λ2,find P{X1 < X2} and P{X2 < X1}.3.) Find P (X > Y) where X and Y are independent random variables that satisfy X~ N (2,1) and Y~ N (6,3)(b) Let Z be a discrete random variable with E(Z) = 0. Does it necessarily follow that E(Z³) = 0? If yes, give a proof; if no, give a counterexample.