In each part, assume the random variable X has a binomial distribution with the given parameters. Compute the probability of the event. (a) n=5,p=0.6 Pr(X=3)= (b) n=3,p=0.2 Pr(X=1)= (c) n=6,p=0.7 Pr(X=3)= (d) n=6,p=0.3 Pr(X=0)=

Compute​ P(X) using the binomial probability formula. Then determine whether the normal 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=56  p=0.5   x=30  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. Use a standard normal distribution table. A. ​P(X)=enter your response here ​(Round to four decimal places as​ needed.)   B. The normal distribution cannot be used.     D) By how much do the exact and approximated probabilities​ differ? A.enter your response here ​(Round to four decimal places as​ needed.) B. The normal distribution cannot be used.   E)By…

If X is a binomial random variable, compute ?(?=?)P(X=x) for each of the following cases:

Let X and Y be independent exponential random variables with parameters 2 and 3. (a) What is the probability that X + Y > 1. (b) Conditional on X + Y = 1, what is the distribution of X.

X is the number of successes in 10 independent Bernoulli trials. The variance of X is equal to 3/4 of the expectation of X (ie Var(X)=0.75E(X)). The probability that X is less than 2 is equal to_____. Please fill in the blank.

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…

Suppose a random variable x is best described by a uniform probability distribution with a range 0 to 5. Find the value of a that makes the following probability statements true.