**Question 5**Suppose a random variable \( X \) has a probability distribution function\[P(X = x) = \begin{cases} \frac{2kx}{x^2 + 1}, & \text{for } x = 2, 3 \\ \frac{kx}{x^2 - 1}, & \text{for } x = 4, 5 \\ 0, & \text{otherwise}. \end{cases}\]where \( k \) is a numerical constant.**Using the value of \( k \), calculate the value of \( F(2.5) \) and \( F(4) \).**- \( \frac{32}{75} \) and \( \frac{8}{9} \)- \( \frac{8}{19} \) and \( \frac{1}{9} \)- \( \frac{8}{33} \) and \( \frac{74}{99} \)- \( \frac{4}{7} \) and \( \frac{37}{21} \)

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Answered: Suppose a random variable X has…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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3. Suppose a certain medical treatment is effective in 80% of the cases treated. Let Y denote the number of patients for which the treatment is effective in a random sample of 100 patients, 100 and p = 0.8. Find an approximate probability that so that Y~ Bin(n, p) with n = 75
Q6. In the following diagram: Họ: µ = 4 ; H1: µ= 1. f(X) Ho Xp Rejection region Non-rejection region Examine the probabilities represented by the regions, a,b and c. Identify the incorrect statement: A. a = Pr(Type I error 'AND’ Not-Type II error). B. a +b = Pr(Type I error). С.с 3D Pr(Туpe Il error). D. a + b + c = Pr(Type I error 'OR’ Type II error) %3D A. A В. В С. С O D. D

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Suppose a random variable X has probability distribution function 2kx 2+1> for x = 2, 3 kr P(X = x) = 72 _]; for ax = 4,5 0, otherwise. where k is a numerical constant. Using the value of k, calculate the value of F(2.5) and F(4). O 32/75 and 8/9 O 8/19 and 1/9 о 8/33 аnd 74/99 O 4/7 and 37/21