13. (Ross, 7.16) Let Z be a standard normal random variable, and for a fixed number...
(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 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)
5. Let Z be a standard normal random variable. Use the table on page 848 of the textbook to evaluate the following. (a) P(Z < 0.04) (b) P (0.09 < 20 S 0.81) (c) P(Z <1.3) (d) P(-2 <7 <1) (e) P(Z -0.1) (Z -0.2) (Z -0.3) (Z-0.4) > 0)
Let Z be a standard normal random variable. Use the calculator provided, or this table, to determine the value of c. P(1.22<Z<c)=0.0703 Carry your intermediate computations to at least four decimal places. Round your answer to two decimal places. 0 X $ ?
number? 10 3. Let X be a continuous random variable with a standard normal distribution. a. Verify that P(-2 < X < 2) > 0.75. b. Compute E(지)· 110]
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.)
(1 point) Let Z be a standard normal random variable. In each of the following, find the number zo which makes the indicated probability statement correct. (a) P(Z zo)-0.9343 Z0 (b) P(-Zo S Z zo) -0,781 Zo - (c) P(-zo K Z K zo) 0.64 Zo (d) P(Z 2 zo) 0.2914 (e) P(-Zo KZ30)-0.2319 (0 P(-1.51SZS zo) 0.5152 Zo
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
Recall from class that the standard normal random variable, Z, with mean of 0 and stan- dard deviation of 1, is the continuous random variable whose probability is determined by the distribution: a. Show that f(-2)-f(2) for all z. Thus, the PDF f(2) is symmetric about the y-axis. b. Use part a to show that the median of the standard normal random variable is also 0 c. Compute the mode of the standard normal random variable. Is is the same...
29. Let Z be a standard normal random variable. (a) Compute the probability F(a) = P(2? < a) in terms of the distribution function of Z. (b) Differentiating in a, show that Z2 has Gamma distribution with parameters α and θ = 2.