The value of Z corresponding to the given probabilities can be obtained from the standard normal distribution table.
a) P(Z c) = 0.025
P(Z < c) = 1 - 0.025
P(Z < c) = 0.975
c = 1.96
b) P(|Z| c) = 0.95
P(-c < Z < c) = 0.95
P(Z < c) = 0.95 + (1 - 0.95)/2
P(Z < c) = 0.975
c = 1.96
c) P(Z > c) = 0.05
P(Z < c) = 1 - 0.05
P(Z < c) = 0.95
c = 1.645
d) P(|Z| c) = 0.9
P(-c < Z < c) = 0.9
P(Z < c) = 0.9 + (1-0.9)/2
P(Z < c) = 0.95
c = 1.645
6. If Z is N(0, 1), find values of c such that: (a) Pr(Z> c)=.025 96...
(4) Given Z N(0, 1) find the following: (a) P(Z 2 1.4) (b) P(Z> 0.75) (c) P(IZI S 2) (d) P(IZ 2 2) (e) Find z such that P(Z < z) = 0.11 (f) Find z such that P(Z > z) = 0.02
3. Let Z be a continuous random variable with Z~ N(0, 1) (a) Find the value of P(Z -0.47) (b) Find the value of P(|Z|< 2.00). Note | denotes the absolute value function. (c) Find b such that P(Z > b) = 0.9382 (d) Find the 27th percentile. (e) Find the value of the critical value zo.05
10. Find the ROC of the Z-transform of x[n] (a) [:l> (6) 31 (0)1> (a) not (a), not (b) and not () 11. Calculate the DFT of the following discrete-time signal with: x[0] = 2, x[1] = -1, x[2] = 3, x[3] = -2. The value of the DFT required for this question is X(0). (a) 2 + j3. (b) 2-4, (c) 6, (d) not (a), not (b) and not e
Part 4 of 10 - Question 4 of 10 1.0 Points Find k such that Pr[Z<k] = .7517, where Z is the standard normal random variable. O A..2483 O B.-.32 Oc..32 O D.-.68 O E..68 Reset Selection
3. Let Z be a continuous random variable with Z~ N(0, 1) (a) Find the value of P(Z < -0.47) (b) Find the value of P(|Z| < 2.00). Note denotes the absolute value function (c) Find b such that P(Z > b) = 0.9382 (d) Find the 27th percentile. (e) Find the value of the critical value z0.05
Find the X2 critical values 12.2 Find the x2 critical values a. C. α-05 n-31 α-10 b. -025 n - 26 α-.10 n 16
Find the following probabilities: a) Pr{Z < 0.66} b) Pr{Z ≥ -0.66} c) Pr{-2.01 < Z < 2.01} d) Pr{-1.91 < Z < 0.0} e) Pr{Z < -1.35 or Z > 1.35} (you want the probability that Z is outside the range -1.03 to 1.03)
Let (In), and (yn).m-1 be sequences such that Pr – yn| < 1/n for all n. Use the definition of convergence to prove that, if (2n)_1 is convergent, then (Yn)-1 is convergent.
Problem 1 (15%): Find the following probabilities for two normal random variables Z = N(0,1) and X = N(-1,9). (a) P(Z > -1.48). (b) P(|X< 2.30) (c) What is the type and the parameters of the random variable Y = 3X +5?
4.28 If Z ~ N(0,1), find the following probabilities: a. P(Z <1.38) b. P(Z > 2.14) c. P(-1.27 <Z<-0.48)