**Problem 7: Probability Distribution of a Discrete Random Variable**A discrete random variable, $ X $, has the following probability distribution:\[\begin{array}{c|c}X & P(X) \\\hline0 & 0.1 \\1 & 0.2 \\2 & 0.4 \\3 & 0.3 \\\end{array}\]**Tasks:**(a) What is the probability that $ X $ is not more than 1?(b) What is the probability that $ X $ is at least 2?(c) Compute $ E(x) $, the expected value of $ x $.(d) Compute $ \sigma^2 $, the variance of $ x $.(e) Compute $ \sigma $, the standard deviation of $ x $.

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7. A discrete random variable, X, has the following probability distribution: X P(X) _0.1 0.2 (a) (b) (c) xxlda 2 3 What is the probability that X is not more than 1? What is the probability that X is at least 2? Compute E(x), the expected value of x. 0.4 0.3

7. A discrete random variable, X, has the following probability distribution: X P(X) _0.1 0.2 (a) (b) (c) xxlda 2 3 What is the probability that X is not more than 1? What is the probability that X is at least 2? Compute E(x), the expected value of x. 0.4 0.3

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

**Problem 7: Probability Distribution of a Discrete Random Variable**

A discrete random variable, $ X $, has the following probability distribution:

\[
\begin{array}{c|c}
X & P(X) \\
\hline
0 & 0.1 \\
1 & 0.2 \\
2 & 0.4 \\
3 & 0.3 \\
\end{array}
\]

**Tasks:**

(a) What is the probability that $ X $ is not more than 1?

(b) What is the probability that $ X $ is at least 2?

(c) Compute $ E(x) $, the expected value of $ x $.

(d) Compute $ \sigma^2 $, the variance of $ x $.

(e) Compute $ \sigma $, the standard deviation of $ x $.

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