A discrete random variable, X, is described by the PMF shown below. a) Determine P[2 < X < 4]. b) Determine P[X = 3] given that 2 < X < 4. c) Graph the CDF of X and label key values. d) Determine E[X]. Show your work! Px(x) 0.2 - 1 2 3 4 5 6 7
Added by Michael F.
Close
Step 1
2 + 0.1 + 0.3 + 0.2 + 0.1 + 0 + 0 = 1 b) To determine P[2 < X < 4], we need to add up the probabilities of X taking values 3 and 4: P[2 < X < 4] = Px(3) + Px(4) = 0.2 + 0.1 = 0.3 c) To determine P[X = 3], we simply look at the PMF: P[X = 3] = Px(3) = 0.3 Show more…
Show all steps
Your feedback will help us improve your experience
Md.Daniyal Arshad and 96 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
Question 1: The CDF of a discrete random variable X is given below. F(x) = 0, for x < 0, 1/16, for 0 <= x < 1, 5/16, for 1 <= x < 2, 11/16, for 2 <= x < 3, 15/16, for 3 <= x < 4, 1 for x >= 4. (a) Find and sketch the PMF of the random variable. (b) Evaluate the probability P[X >= 1 | X <= 4]
David N.
A discrete random variable X has the cdf as follows F(x) = 0 x < 0 0.06 0 <= x < 1 0.19 1 <= x < 2 0.39 2 <= x < 3 0.67 3 <= x < 4 0.92 4 <= x < 5 0.97 5 <= x < 6 1 x >= 6 Calculate a. [4 points] The probability mass function (pmf) f(x) b. [3 points] P(X > 3) c. [3 points] P(2 < X <= 5)
Thuc N.
4. Suppose X is a discrete random variable with the CDF defined as Fx(x) = { 0, x < 0 1/5, 0 <= x < 1 8/15, 1 <= x < 2 14/15, 2 <= x < 3 1, 3 <= x } (a) Draw the CDF. Then calculate: (b) P(1 < X <= 3) (c) P(1 <= X <= 3) (d) P(X = 2) (e) P(X > 2) (f) What is the probability mass function of X? (g) Find E(X).
Ahmet Y.
Recommended Textbooks
Elementary Statistics a Step by Step Approach
The Practice of Statistics for AP
Introductory Statistics
Watch the video solution with this free unlock.
EMAIL
PASSWORD