A)For n=56​, p=0.5​, and X=30, use the binomial probability formula to find​ P(X).     B)Can the normal distribution be used to approximate this​ probability? A. ​No, because np(1−p)≤10   B. ​Yes, because np(1−p)≥10   C. ​Yes, because np(1−p)≥10   D. ​No, because np(1−p)≤10   C) Approximate​ P(X) using the normal distribution.

f(x) = (2x + 1)/c, 0 ≤ x ≤ 4. Find the variance of the distribution. 438/c² 409.2/c² O 431.6/c² O 419.6/c²

The geometric distribution gives the probability that the first success occurs at the xth trial with success probability p. f(x)=(1-p)x-1p, x=1,2,3,... Show that E(X)=1/p

The random variable X takes value O with probability, and value 1 with the remaining probability. The random variable Y takes value 100 with probability and value 101 with the remaining probability. What is the relation between the variance of X and the variance of Y? Var[X] Var[Y] "

Q1A Suppose that the probability of finding defectives within a manufactured lot of electrical fuses is 0.09. Assume the probability distribution function (PDF) is binomial. Let X be the number of defectives within the sample. In a sample of 25 fuses, find the probabilities: (a) P(X 2), (b) P(X > 0), (c) P(1 ≤ X < 4). === B Suppose the discrete random variable X has the PDF as in the table below. Find: (a) F(7), (b) E(4-3X). I 4 6 7 8 9 f(x) 0.2 0.25 0.15 0.3 0.1

min {X1, X2}. %3D Suppose that X1, X2 are iid, and X1 Exp(2). Find the distribution of X(1)

Compute P(X) using the binomial probability formula. Then detemine whether the nomal distribution can be used to estimate this probability. If so, approximate P(X) using the normal distribution and compare the result with the exact probability. n= 40, p= 0.35, and X= 25 ...... . P(X)=(Round to four decimal places as needed.) Can the normal distribution be used to approximate this probability? O A. Yes, the normal distribution can be used because np(1- p)<10. O B. No, the normal distribution cannot be used because np(1 - p)< 10. O C. Yes, the normal distribution can be used because np(1-p) 10. O D. No, the normal distribution cannot be used because np(1-p) 2 10. Approximate P(X) using the normal distribution. Use a standard normal distribution table. Select the correct choice below and fill in any answer boxes in your choice. O A. PX)=A (Round to four decimal places as needed.) O B. There is no solution. By how much do the exact and approximated probabilities differ? Select the correct…