Question

Consider the following discrete random variables: (a) X has a Bernoulli distribution, with P[X = 1] = 2/3, P[X = 0] = 1/3 (an unfair coin toss). (b) X takes the values 1,2,3,4,5, and 6, with each outcome equally likely, P(X = j) = 1/6 for j = 1,2,3,4,5,6 (the result of rolling a fair, six-sided die). (c) X takes the value 1,2,3,4, and 6, with P(X = j) = 1/6 for j = 1,2,3,4, and P(X = 6) = 1/3 (the result of rolling a loaded die that will never land on 5). For each of the above examples: (a) Graph the probability mass function; (b) Write down the equation for the cdf Fx. Graph Fx. What is the support of the distribution of X? What is P(X < 1)? What is P(X < 3)? What is P(X ∈ {1,3,5})? What is P(1 < X ≤ 3)? (h) What is P(1 ≤ X ≤ 3)? What is E(X)?

          Consider the following discrete random variables: (a) X has a Bernoulli distribution, with P[X = 1] = 2/3, P[X = 0] = 1/3 (an unfair coin toss). (b) X takes the values 1,2,3,4,5, and 6, with each outcome equally likely, P(X = j) = 1/6 for j = 1,2,3,4,5,6 (the result of rolling a fair, six-sided die). (c) X takes the value 1,2,3,4, and 6, with P(X = j) = 1/6 for j = 1,2,3,4, and P(X = 6) = 1/3 (the result of rolling a loaded die that will never land on 5).
For each of the above examples: (a) Graph the probability mass function; (b) Write down the equation for the cdf Fx. Graph Fx. What is the support of the distribution of X?
What is P(X < 1)? What is P(X < 3)? What is P(X ∈ {1,3,5})? What is P(1 < X ≤ 3)? (h) What is P(1 ≤ X ≤ 3)? What is E(X)?

Added by Chase C.

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