Question

A discrete random variable X has the following probability distribution: xi 13 18 20 24 27 PX (xi) = P(X = xi) 0.12 0.35 0.2 0.11 0.22 Compute each of the following quantities. 1) P(x < 24) 2) P(x ≤ 24) 3) P(x > 20) 4) P(x ≤ 20) 5) The expectation E(X) 6) The expectation of X2 (i.e; E(X2)) 7) The expectation of 3X + 1 (i.e; E(3X + 1)) 8) The expectation of 2√X − 1 (i.e; E(2√X − 1)) 9) The variance V (X) 10) The standard deviation σ(X) 11) The variance of 3X + 1 (i.e; V (3X + 1)).

          A discrete random variable X has the following probability distribution:
xi 13 18 20 24 27
PX (xi) = P(X = xi) 0.12 0.35 0.2 0.11 0.22
Compute each of the following quantities.
1) P(x < 24)
2) P(x ≤ 24)
3) P(x > 20)
4) P(x ≤ 20)
5) The expectation E(X)
6) The expectation of X2 (i.e; E(X2))
7) The expectation of 3X + 1 (i.e; E(3X + 1))
8) The expectation of 2√X − 1 (i.e; E(2√X − 1))
9) The variance V (X)
10) The standard deviation σ(X)
11) The variance of 3X + 1 (i.e; V (3X + 1)).

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Added by Teresa W.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Bradley Duda

05/28/2024

Step 1

Given Data: - \( x_i: 13, 18, 20, 24, 27 \) - \( P(X = x_i): 0.12, 0.35, 0.2, 0.11, 0.22 \) Show more…

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A discrete random variable X has the following probability distribution: xi 13 18 20 24 27 PX (xi) = P(X = xi) 0.12 0.35 0.2 0.11 0.22 Compute each of the following quantities. 1) P(x < 24) 2) P(x ≤ 24) 3) P(x > 20) 4) P(x ≤ 20) 5) The expectation E(X) 6) The expectation of X2 (i.e; E(X2)) 7) The expectation of 3X + 1 (i.e; E(3X + 1)) 8) The expectation of 2√X − 1 (i.e; E(2√X − 1)) 9) The variance V (X) 10) The standard deviation σ(X) 11) The variance of 3X + 1 (i.e; V (3X + 1)).

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