? = n * p = 35 * 0.4 = 14
? = sqrt(n * p * (1 - p)) = sqrt(35 * 0.4 * 0.6) = 2.9
= P(Z < 0.86)
= 0.8051
5. A random variable X follows a binomial distribution with n 35 and p-4. Use the...
A. Random variable X has a binomial distribution, B(36, 0,5). Use the normal approximation, Compute P[15Kx<19)- B. Random variable X has a normal distribution, N(50, 100) Compute P(X < 41 or X>62.0)
QUESTION 8 Let x be a binomial random variable with n=5 and p=0.7. Find P(X <= 4). O 0.1681 0.5282 0.4718 0.8319 0.3601
Let X be a discrete random variable that follows a Poisson distribution with = 5. What is P(X< 4X > 2) ? Round your answer to at least 3 decimal places. Number
5. Imagine a random variable X that has a binomial distribution with n = 12 and p = 0.4. Determine the following probabilities a) P(X 5) b) P(X s2) c) P(X9) d) P (3 X<5)
2. Let X be a binomial random variable with n 18 and p 0.48. Find (а) Р(X — 17) (b) Р(14 < X < 22) (c) the largest integer m such that P(X > m) > 0.7. You could do this by trial-and-error or by automating the process with for loop
7. If x is a binomial random variable find the following probabilities: a) P(x = 2) n = 10 and p = .40 b) P (x < 5) for n = 15 and p = .60 8. Find pl, oland o for n = 25 and p = .50
Exercise 2 Consider a random variable X with E]5 and VarX 16 (a) Calculate P(lz-5 < 6) if X follows a normal distribution. (b) Use Chebyshev's inequality to provide a lower bound for P(-5). (No longer assume X is normal.)
(1 point) If X is a binomial random variable, compute the probabilities for each of the following cases: (a) P(X < 3), n = 9, p = 0.3 Probability = (b) P(X > 4), n = 5, p = 0.3 Probability = (c) P(X<5), n = 7.p = 0.35 Probability = (d) P(X > 6), n = 7, p = 0.3 Probability =
5. Suppose that the probability distribution function (p.d.f.) of a random variable X is as follows: a-x3) for 0<x<1 o/w Sketch this p.d.f. and determine the values of the following probabilities: f(x) =
Problem 7 (15 points). Let X be random variable with the binomial distribution with parameters n and 0 <p<1. (1) Show that **- 1 = 2* for any 1 Sxsn. (2) Show that when 0 < x < (n + 1)p, P(X = x) is an increasing function x and for (n + 1)p <x Sn, P(X = x) is a decreasing function x. (3) A certain basketball player makes a foul shot with probability 0.80. Determine for whal value...