8. For each of the following calculate the quantity indicated. [4 points each) (a) Suppose that...
4 Suppose X-Poisson(2) and if ρ(6)sp(7), then a Find the parameter λ (8 points) el Calculate the p(0) [7 points] IO pr 21Page
4. (8 Marks) Suppose X is a random variable best described by a uniformly distribution or probability that ranges from 2 to 11. a) Write down the probability density function f(1). (1.5 points) b) Compute the following: i) mean (1.5 points) ii) standard deviation (1.5 points) iii) P(X < 3.858) (1.5 points) iv) P(-O< X <H+ o) (2 points)
Suppose that the cdf of random variable X is Skex-3, X <4 11, X >4 Find k. (2 Points) Find the expected value of X. (2 Points)
(e) Suppose that 4 balls are placed sequentially into one of 5 bins, where the bin for each ball is selected at random. For i = 1, 2,3,4,5, define the indicator variables 1, if the ith bin is empty; 0, otherwise Xi _ Then the number of empty boxes is given by X = X\+X2+ X3 + X4+X5, and we learned from week #7 lecture notes and midterm II that Xi ~ Bernoulli(p) with p = (1 - 2)4 =...
3. Suppose that X has a Poisson distribution with mean μ=15. Use the 'cdf' command MTB > cdf; SUBC 〉 poisson 15. Find PX 〈 10)-[3] and P(15 X 20)= [3] 4. Suppose that Y has a hypergeometric distribution with parameters N = 20, M = 6, and n = 4, Use the command MTB > cdf 3; hypergeometric 20 6 4. a. [3] to find P(Y 53) = b. 3) Use the similar command to find P(Y > 2)...
a) In each of the following pmfs, find the value of C. i) p(x) Cx, x 1, 2, 3, 4, 5 ii) p(x) C/x, 2,4,8, 16 b) Assume that the pmf of a discrete random variable X is given by px (x) = 20x-, x = 1, 2, 3, Calculate the following probabilities: i) P(X <3) ii) E[X]
8. Suppose that the joint density of X and Y is given by e if 0< I<, 0<y< 0, otherwise. Find P(X > 1 Y = y).
18. [-12 Points] DETAILS 0/6 Submissions Used Find the indicated set if given the following. A = {x|* 2 -4} B = {x|x <6) C = {xl -1 < x 57} (a) BUC O {xl x < 7) • {xx57) {x|6<x< 7) O {xl 6 SX57) all real numbers none of these (b) BAC {xl-4 < x <6) {x\-4 SX 56) {x{-1<x<6) {x-1556) all real numbers ООО none of these Mand Helm Type here to search O RI 99 a
Need the answers diagramed
6) Find the indicated probabilities. [3pts. each] a) P(z < 1.28) b) P(-2.15 z 1.55) c) P(z> 1.64) d) ? = 5.5, ? = .08, P(5.36 < x < 5.64) e) ?--8.2, ?-7.84, P(x-5.00) 18.5, ? 9.25, P(x < 5.24) tion 3nts
7T Problem [1] <15 points> -ĉ on a surface given by r = 5—10,0=1,2=4 →8. Calculate the total flux Ø passing through this surface. Magnetic flux density is given as B = 92 6+92 r r