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- Let X and Y are independent Poisson random variables such that E(X) = E(Y)=2. Let Z=X+Y. Compute P(X=2|Z=3).Exercise 3. Let X be a random variable with mean µ and variance o². For a € R, consider the expectation E((X − a)²). a) Write E((X - a)²) in terms of a, μ and σ². b) For which value a is E((X − a)²) minimal? c) For the value a from part (b), what is E((X − a)²)?Let X be a random variable. Which of the following statement is INCORRECT? If V (X) = 0, then there exists an x, such that Pr(X = x) = 1. There are cases that V(X) does not exist. By the definition of the random variable, the range of X is a subset of R; therefore, there must exist at least one x such that Pr(X = x) > 0. If Pr(X = 1) (E(X))².
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- Three alleles (alternative versions of a gene) A, B, and O determine the four blood types A (AA or AO), B (BB or BO), O (OO), and AB. The Hardy-Weinberg Law states that the proportion of individuals in a population who carry two different alleles is P=2pq+2pr+2rq where p,q, and r are the proportions of A, B, and O in the population. Use the fact that p+q+r=1 to find the maximum value of P. (DO NOT USE LAGRANGE MULTIPLIERS)A2he joint pat of the random variable X and Yis iven in the below matrix. Find the mean value f X and Y: P(X,Y)= X 2.45 and 2.1 1.9 and 2.45 O 1.9 and 2.1 2.1 and 2.45 Y 0.05 0.05 0.1 0.05 0.1 0.35 0 0.2 0.1
