3. (8 pt, 2 each) (Ross) Let X be a random variable taking values in the...
Let X be a discrete random variable taking integer values 1, 2, ..., 10. It is also known that: P(X < 4) = 0.57, PCX 2 4) = 0.71. Then P(X = 4) = A: 0.14|B: 0.28 |C: 0.45 OD: 0.64|E: 0.73 OF: 0.95 Submit Answer Tries 0/5
2.6.11. Adegenerate random variable is a random variable taking a constant value Let X= c. Show that E(X)=c, and Var(X)=0. Also find the cumulative distribution function of the degenerate distribution of X.
Determine whether the random variable is discrete or continuous. In each case, state the possible values of the random variable. (a) The number of points scored during a basketball game. (b) The amount of rain in City B during April. (a) Is the number of points scored during a basketball game discrete or continuous? A. The random variable is discrete. The possible values are x≥0. B. The random variable is continuous. The possible values are x =0, 1, 2..... C. The random variable is discrete. The...
LetX be a random variable that takes on values between 0 and c. (i.e P(0 X-c)-1). Show that Var(X) . Hint: You may want to first argue that EX21S cklX), and then use this inequality to show that Var(X)-C2 1 to show that Var(x)sa*X (i- E
5. Doing (much) Better by Taking the Min Let X be a random variable that takes on the values in the set {1,...,n} that satisfies the inequality Pr( x i) Sali for some value a>0 and all i € {1,...,n}. Recall that (or convince yourself that) E(X) = P(X= i) = Pr(x2i). 1. Given what little you know so far, give the best upper bound you can on E(X). 2. Let X1 and X2 be two independent copies of X...
Problem 3. Let X be a discrete random variable, gx) - a+ bX+ cX, and let a. b, c be constants. Prove, using the definition of expectation of a function of a random variable, namely , that E(a + bX + cx?) = a + bE(X) + cE(X2)
Please select 2 & 3 2. Let X and Y be discrete random variables taking values 0 or 1 only, and let pr(X = i, Y = j)-pij (jz 1,0;j = 1,0). Prove that X and Y are independent if and only if cov[X,Y) 0 3. If X is a random variable with a density function symmetric about zero and having zero mean, prove that cov[X, X2] 0.
6. Let X be an exponential random variable with parameter 1 = 2. Compute E[ex]. = 7. Consider a random variable X with E[X] u and Var(X) 02. Let Y = X-4. Find E[Y] and Var(Y). The answer should not depend on whether X is a discrete or continuous random variable.
2. For a discrete random variable X, with CDF F(X), it is possible to show that P(a < X S b)-F(b) - F(a), for a 3 b. This is a useful fact for finding the probabil- ity that a random variable falls within a certain range. In particular, let X be a random variable with pmf p( 2 tor c-1,2 a. Find the CDF of X b. Find P(X X 5). c. Find P(X> 4). 3. Let X be a...
1 Let X be a discrete random variable. (a) Show that if X has a finite mean μ. then EX-ix-0. (b) Show that if X has a finite variance, then its mean is necessarily finite 2 Let X and Y be random variables with finite mean. Show that, if X and Y are independent, then 3 Let Y have mean μ and finite variance σ2 (a) Use calculus to show that μ is the best predictor of Y under quadratic...