Problem 5 [10%] A discrete random variable N has probability density function P(N=n) = { c/n, n=1,2,3,4 0, otherwise 1. Find the value of the constant c. 2. Find P(N=1) 3. Find P(N ? 2)
Added by -Ngeles B.
Close
Step 1
We know that the sum of all probabilities for a discrete random variable must equal 1. So, we have: c * (1/1 + 1/2 + 1/3 + 1/4) = 1 Now, we can find the value of c by solving this equation: c * (1 + 1/2 + 1/3 + 1/4) = 1 c * (25/12) = 1 Divide both sides by Show more…
Show all steps
Your feedback will help us improve your experience
T. L. and 77 other Intro Stats / AP Statistics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
1.Suppose that a random variable X has a discrete distribution with the following probability mass function: f(x) = cx if x = 1, 2, 3, 4, 5 f(x)=0, otherwise Determine the value of the constant c. 2. Suppose X ∼ N (100, 5 2 ). Find P(95 ≤ X ≤ 110).
Adi S.
Problem 2: The random variable N has PMF n = {1, 2, 3, ...} Pv(n) = 0, otherwise. (a) What is the value of the constant c? (b) What is the value of P[N ≤ 2]? (c) What is the value of P[N ≥ 2]?
Robin C.
Problem 3 (2 marks): The probability density function of a random variable X is given by f(x) = 0.22 for x > 5, and 0 otherwise. Find P(X > 10); Find E(X); Find the CDF of X; If X1, X2, X3 are independent and identically distributed random variables with the same probability density function as above, what is the probability that at least 2 of these 6 random variables will be bigger than 10? Problem 4 (2 marks): Let X1 and X2 be independent random variables, each following an exponential distribution with mean Α. Find P(min{X1, X2} > 1). (Hint: min{X1,X2} > 1 is equivalent to X1 > 1 and X2 > 1)
Sri K.
Recommended Textbooks
Elementary Statistics a Step by Step Approach
The Practice of Statistics for AP
Introductory Statistics
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD