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(20 points) Let Z be a standard normal random variable and X -ZI(Z). Find E(X) (a, o0) (20 points) Let Z be a standard normal random variable and X -ZI(Z). Find E(X) (a, o0)
Let z be a random variable with a standard normal distribution. Find P(0 ≤ z ≤ 0.40), and shade the corresponding area under the standard normal curve. (Use 4 decimal places.)
Let z be a random variable with a standard normal distribution. Find the indicated probability. (Round your answer to four decimal places.) P(z ≤ −1.94) = [x].
Let Z be a standard normal random variable and (z) be the c.d.f. of Z. (a) Find the constant c such that Ф(c)-0162, (b) Find z03
1) Let Z be the standard normal variable. Find the values of z if z satisfies the given probabilities. (Round your answers to two decimal places.) (a) P(Z > z) = 0.9706 z = ? P(−z < Z < z) = 0.8164 z = ? 2) Suppose X is a normal random variable with μ = 350 and σ = 20. Find the values of the following probabilities. (Round your answers to four decimal places.) (a) P(X < 405) = (b) P(370...
Let the random variable Z follow a standard normal distribution. Find P(-2.35 < Z< -0.65). Your Answer:
6. Let Z's be independent standard normal random variables. (a) Define X = Σ Z f X. (b) Define Y = 4 Σ zi. Find the mean and variance of Y. (Hint: Use the fact E(Z Z,)-0 for any i fj, i,j 1,2,3,4.) i. Find the mean and variance o i=1 4 i=1
Let Z be a standard Normal random variable. Then for non-random numbers a and b. the random variable X-a Z+bhas the distribution ON(b, a) ON(b,a) ON(a, B) ON(a,b)
1. Let Z be the standard normal random variable. Find (a) P(Z > −1.78) = (b) P(−.60 < Z < 1.25) = (c) z.005 = (d) z.025 =
Question 32 Let Z be the standard normal random variable. Find z so that the area to the left of z is 0.0250 O-1.81 O 1.28 None of the above
Let z be a random variable with a standard normal distribution. Find the indicated probability. (Round your answer to four decimal places.) P(−1.24 ≤ z ≤ 2.64) = Shade the corresponding area under the standard normal curve.