2. Let Z~ N(0,12) (distributed as a standard normal rv). Calculate the following probabilities, show your...
4. Let Z ~ N(0,1) be a standard normal variable. Calculate the probability (a) P(1 <Z < 2). (b) P(-0.25 < < < 0.8). (c) P(Z = 0). (d) P(Z > -1).
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 and calculate the following probabilities, drawing pictures wherever appropriate.a. \(P(0 \leq Z \leq 2.17)\)b. \(P(0 \leq Z \leq 1)\)c. \(P(-2.50 \leq Z \leq 0)\)d. \(P(-2.50 \leq Z \leq 2.50)\)e. \(P(Z \leq 1.37)\)f. \(P(-1.75 \leq Z)\)g. \(P(-1.50 \leq Z \leq 2.00)\)h. \(P(1.37 \leq Z \leq 2.50)\)i. \(P(1.50 \leq Z)\)j. \(P(|Z| \leq 2.50)\)
Standart Normal Probabilities
Let Z be a standard normal random variable. Calculate the following probabilities using the calculator provided. Round your responses to at least three decimal places. P(Z >-2.11) P(Z 1.82) = P (-048<Z < 205) Clear Undo Help Next>> Explain
1. Let 2 ~ N (0,1). Using a standard normal table, find the following probabilities. You do not need to provide any equation. Instead, draw pictures as we did in the lecture and find the numbers from the table. Make yourself be familiar with using different kinds of tables. (Hint: The standard normal density is symmetric around zero.] (a) P(Z < 0) (b) P(Z < 1.96) (c) P(Z < 1.96) (d) P(Z = 1.96) (e) P(-1.65 < 2 <0) (f)...
1. Given that z is a standard normal random variable, compute the following probabilities. a. P(Z < 1.38) b. P(z 2 1.32) c. P(-1.23 Sz5 1.23)
Let Z be a standard normal random variable and
calculate the following probabilities, drawing pictures whenever
appropriate. (Do this on paper. Your instructor may ask you to turn
in this work.)
(a) P(0 Z
2.74)
(b) P(0 Z
1)
(c) P(-2.40 Z
0)
(d) P(-2.40 Z
+2.40)
(e) P(Z 1.63)
(f) P(-1.74 Z)
(g) P(-1.4 Z
2.00)
(h) P(1.63 Z
2.50)
(i) P(1.4 Z)
(j) P( |Z| 2.50)
Let Z be a standard normal random variable and calculate the following...
A) 0.7995 11. If Z is a standard normal variable find the probabilities of a) P(Z <-0.35)- @w B) 0.3982 C) 1.2008 D) p.4013 (2 points) b) P(0.25s Z<1.55) (3 points) c) P(Z > 1.55) (2 points) 12. Assume that X has a normal distribution with mean deviation .5. Find the following probabilities: 15 and the standard a) P(X < 13.50)- 3 points). b) P (13.25 <X < 16.50)- (5 points). B) 0 2706 C0 5412 D) 1.0824 A mountuin...
Let Z be a standard normal random variable and calculate the following probabilities, drawing pictures wherever appropriate. (Round your answers to four decimal places.) (a) P(0 ≤ Z ≤ 2.64) (b) P(0 ≤ Z ≤ 2) .4772 Correct: Your answer is correct. (c) P(−2.10 ≤ Z ≤ 0) (d) P(−2.10 ≤ Z ≤ 2.10) (e) P(Z ≤ 1.94) (f) P(−1.45 ≤ Z) (g) P(−1.10 ≤ Z ≤ 2.00) (h) P(1.94 ≤ Z ≤ 2.50) (i) P(1.10 ≤ Z) (j) P(|Z|...
2. The Markov chain (Xn, n = 0,1, 2, ...) has state space S = {1, 2, 3, 4, 5} and transition matrix (0.2 0.8 0 0 0 0.3 0.7 0 0 0 P= 0 0.3 0.5 0.1 0.1 0.3 0 0.1 0.4 0.2 1 0 0 0 0 1 ) (a) Draw the transition diagram for this Markov chain.