Question 3. Let X be a discrete random variable with the following probability mass function (pmf): x 0 1 2 4 P(X=x) 0.1 0.4 0.3 0.2 Find the following: (a) P(X = 3) (b) P(X ? 2.99) (c) The expected value of Y = (X-2)/2 (d) The cumulative distribution function (cdf) of X. Sketch also its graph.
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Since there are three probabilities given (0.1, 0.3, and 0.2), there must be three possible values for X. Let's call these values x1, x2, and x3. Then, the pmf can be written as: P(X = x1) = 0.1 \\ P(X = x2) = 0.3 \\ P(X = x3) = 0.2 Now, let's answer the Show more…
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Question 3. Let X be a discrete random variable with the following probability mass function (pmf): x 0 1 2 4 P(X=x) 0.1 0.4 0.3 0.2 Find the following: (a) P(X = 3) (b) P(X ≤ 2.99) (c) The expected value of Y = (X-2)/2 (d) The cumulative distribution function (cdf) of X. Sketch also its graph.
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