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The random variable Y has the following probability distribution. k Pr(Y = k) 3 6 9...
3. (10 points) The random variable Y has a normal probability distribution with the density function (a) Verify,Ef(y) dy=1; (b) Show that E(Y) = μ; (c) Let F(u) be the distribution function of Y. Prove that e2 1 dr 3. (10 points) The random variable Y has a normal probability distribution with the density function (a) Verify,Ef(y) dy=1; (b) Show that E(Y) = μ; (c) Let F(u) be the distribution function of Y. Prove that e2 1 dr
3. If a random variable Y has a Chi-square distribution with 9 degrees of freedom. a) The mean of the distribution is b) The standard deviation of the distribution is c) The probability, p( y = 5) = d) The probability, P(Y>8 ) = e) the probability, p( y < 2) = _
2. (10 points) The random variable X has the following probability distribution x 2 3 5 8 Pr(X = x) 0.2 0.4 0.3 0.1 a) Pr (X<=3) P(X<=3) b) Pr( 2.7<X<5.1) c)Pr(X>2.5) d) E(X)
A random variable K has probability distribution [a] What value of C will make this a discrete probability density?[b] If n = 4, what is the E(K)? Hint: Consider sums of powers of the first n integers.
that makes the following probability statements true. Suppose a random variable T is best described by a uniform probability distribution with range 2 to 5. Find the value of (a) PIS a) = 0.96 (b) Pr<a) = 0.54 (c) P(12 a) = 0.21 (d) P(x > a) = 0.19 (e) P(2.74 SIS a) = 0.21
Let the random variable Y have the following probability distribution y 2 4 6 P(Y=y) 4/k 1/k 5/k find the value of k. find the moment-generating function of Y find Var(Y) using the moment generating function let W= 2Y-Y^2 +e^2*Y+7. find E(W)
3. The probability distribution of the discrete random variable X is f(x) = 2 x 1 8 x 7 8 2−x , x = 0, 1, 2. Find the mean of X. 4. The random variable X, representing the number of errors per 100 lines of software code, has the following probability distribution: x 1 2 3 5 6 f(x) 0.03 0.37 0.2 0.25 0.15 (a) Find E(X). (b) Find E(X2 ). 5. Use the distribution from Problem 4. (a)...
Below is the probability distribution for random variable x. What is the probability of at least a score of 2 in this distribution? X 1 2 3 P(x) 0.18 0.42 0.40 a. .82. b. .18. c. .42. d. .60.
I . (20%) Random variable X has the probability density function as ; Random variable Y 2X+1 0 otherwise a) Determine A b) Determine the Probability Distribution Function F, (x) c) Determine E(X) and ơx d) Determine the probability density function fy(y) and E(Y)
A random variable X has a distribution with probability function f(x) = K(nx)2x for x = 0,1,2,...,n where n is a positive integer. a. Find the constant k. b. Find the expected value M(S) = E(esX) as a function of the real numbers s. Compare the values of the derivative of this function M'(0) at 0 and the expected value of a random variable having the probability function above. c. What distribution has probability function f(x)? Let X1, X2 be independent random variables both...