solve all the questions with details. Let X be a geometric random variable. If P(X>7| X-4)-0.216,...
Let X be a geometric random variable with p = 0.83. Use your calculator to find PX < 4)
3. Let X be a geometric random variable with parameter p. Prove that P(X >k+r|X > k) = P(X > r). This is called the memoryless property of the geometric random variable.
QUESTION 4 Suppose Xis a random variable with probability density function f(x) and Y is a random variable with density function f,(x). Then X and Y are called independent random variables if their joint density function is the product of their individual density functions: x, y We modelled waiting times by using exponential density functions if t <0 where μ is the average waiting time. In the next example we consider a situation with two independent waiting times. The joint...
2040DE_Quiz3_DiscreteRV Let X be a discrete random variable that follows a geometric distribution with p = 0.44. What is P(X < 3)? Round your answer to at least 3 decimal places. Number
3. Let X be a random variable from a geometric distribution with parameter p (P(X- k p(1-P)"-, } k-1 k-1, 2, ...). Find Emin{X, 100
Let X be the random variable with the geometric distribution with parameter 0 < p < 1. (1) For any integer n ≥ 0, find P(X > n). (2) Show that for any integers m ≥ 0 and n ≥ 0, P(X > n + m|X > m) = P(X > n) (This is called memoryless property since this conditional probability does not depend on m.)
Question 1: 1a) Let the random variable X have a geometric distribution with parameter p , i.e., P(X = x) = pq??, x=1,2,... i) Show that P(X > m)=q" , where m is a positive integer. (5 points) ii) Show that P(X > m+n X > m) = P(X>n), where m and n are positive integers. (5 points) 1b) Suppose the random variable X takes non-negative integer values, i.e., X is a count random variable. Prove that (6 points) E(X)=...
A discrete random variable X follows the geometric distribution with parameter p, written X ∼ Geom(p), if its distribution function is A discrete random variable X follows the geometric distribution with parameter p, written X Geom(p), if its distribution function is 1x(z) = p(1-P)"-1, ze(1, 2, 3, ). The Geometric distribution is used to model the number of flips needed before a coin with probability p of showing Heads actually shows Heads. a) Show that fx(x) is indeed a probability...
1) Let x be a continuous random variable that is normally distributed with a mean of 21 and a standard deviation of 7. Find to 4 decimal places the probability that x assumes a value a. between 24 and 30. Probability = b. between 17 and 31. Probability = ------------------------------------------------------------------------------------------------------------------------------------------------------ 2) Let x be a continuous random variable that is normally distributed with a mean of 65 and a standard deviation of 15. Find the probability that x assumes a...
Question 5 The following table contains values of the c.d.f. for the random variable X, which has a geometric distribution with parameter p = 0.4. Choose the option that gives a correct statement about X. x 1 2 3 4 5 6 ... F(x) 0.4 0.64 0.784 0.8704 0.9222 0.9533 ... A q0.8 = 4 B q0.95 = 5 C m = 3.5 D iqr = 0.384 E None of the above Question 16 The random variable X has a...