A random variable, z, has p.d.f. f (z) = e¯², 0 =< Z < 1. Calculate the expected value of z. a. 1 b. 4.76 no O O d. 0
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- Suppose the random variable X follows a normal distribution with mean 70 and variance 100. Then the probability is 0.6826 that X is in the symmetric interval about the mean between two numbers are O A. None O B. 70 and 90 O C. -1 and 1 OD. 60 and 80Which of the following are true when considering the probability of spinning a multiple of 5 on an equal section spinner with numbers 1-20? which apply. a. P(A) = ⅕ b. n(S) = 20 c. n(A) = 4 d. n(A’) = 16 e. P(A) = 20% f. A = {5,10,15,20} g. P(A) = 4/20 h. P(A’) = ⅘ i. P(A’) = 0.8 j. S is all numbers between 1 and 20 inclusiveSuppose that a discrete random variable X has a distribution with the following probability (4cx,x = 2,3,5 ( 0, otherwise function: f(x) a. Determine the value of the constant c: b. Calculate Pr (X > 3) (please use the value of c from part a.):
- A random variable, z, has p.d.f. f (z) = e ², 0 =< z < 1. Calculate the expected value of z. a. 1 O b. 4.76 O C. no O d. 0Let X₁ and X₂ be independent r.v.'s having the same distribution, taking on values 0 and 1 with respective probabilities 0.2 and 0.8. Answer Questions 12 and 13 below. Question 12 Write the m.g.f. of X₁ + X₂ + 2. (0.2+0.8e²) ²% e²z ○ (0.2e + 0.8e²x) e²z (1 + 0.² e² )² e²² (0.2+0.8e²)² e²z Question 13 Write the m.g.f. of X₁ – 2X₂. (0.2 +0.8e²) (0.2 +0.8e-2²) (0.8e + 0.2e²) (0.2e + 0.8e-2²) (0.2e +0.8e²) (0.2e-² +0.8e-²²) O (0.2e² +0.8e-²) (0.2e + 0.8e²)The following table provides the joint probability distribution of of X and Y y3(-1 tion 1 1 3 3 then cov(x,y) none 3. 3. 1130
- Let X1, . . . , X7 independent random variables with exponential distribution of parameter λ = 2. What distribution has the next sum?2 of 4 (0 complete) Using the data given below, determine whether it would unusual for a household to have no HD televisions. The number of televisions (HD) per household in a small town Televisions 1 Households 26 445 655 1474 P(x) 0.010 0.171 0.252 0.567 Choose the correct answer below. O A. It would be unusual because the probability of having no HD televisions is less than 0.05. O B. It would not be unusual because the probability of having no HD televisions is more than 0.05. OC. It would not be unusual because 26 people have no HD televisions in the town. O D. It would be unusual because 26 people have no HD televisions in the town. Click to select your answer.Let X1, X2, ... be a sequence of random variables with finite mean u and non-zero variance o?. Let S, = X;. Which random variable has meanequal to 0 and variance - equal to 1? Select one: S-np O a. Zn Vno Sn-H O b. Zn Vno O c. Zn Vño O d. Zn Vno