1) Suppose random variable X - N(2,4) (normal distribution with mean 2 and variance 4). Suppose random variable Y follows the distribution below (0 and 1 are the only two possible outcomes for Y): (0.4 Pr(Y = y) = (0.6 What is Pr(X=1) and Pr(Y=1) respectively? y = 0 y = 1
1) Suppose random variable X - N(2,4) (normal distribution with mean 2 and variance 4). Suppose random variable Y follows the distribution below (0 and 1 are the only two possible outcomes for Y): (0.4 Pr(Y = y) = (0.6 What is Pr(X=1) and Pr(Y=1) respectively? y = 0 y = 1
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![### Probability Distributions and Calculations
**Problem Statement:**
1. **Suppose** random variable \( X \sim \mathcal{N}(2,4) \) (normal distribution with mean 2 and variance 4).
Suppose random variable \( Y \) follows the distribution below (0 and 1 are the only two possible outcomes for \( Y \)):
\[
\Pr(Y = y) =
\begin{cases}
0.4 & \text{if } y = 0 \\
0.6 & \text{if } y = 1
\end{cases}
\]
What is \( \Pr(X=1) \) and \( \Pr(Y=1) \) respectively?
**Explanation:**
- **\( X \) Distribution:**
\( X \) is normally distributed with a mean (\( \mu \)) of 2 and a variance (\( \sigma^2 \)) of 4. This distribution, denoted as \( \mathcal{N}(2,4) \), tells us about the spread and central tendency of \( X \).
- **\( Y \) Distribution:**
\( Y \) is a discrete random variable with two possible outcomes: 0 and 1. The probability distribution for \( Y \) is clearly specified:
- \(\Pr(Y = 0) = 0.4\)
- \(\Pr(Y = 1) = 0.6\)
**Questions:**
- **\( \Pr(X = 1) \):**
The question asks for the probability that the normally distributed variable \( X \) equals 1. Since the normal distribution is continuous, \(\Pr(X = 1)\) is technically zero because continuous distributions measure the probability of intervals rather than exact values.
- **\( \Pr(Y = 1) \):**
According to the provided distribution, \(\Pr(Y = 1) = 0.6\).
This problem examines understanding of both continuous and discrete probability distributions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F03191458-7d30-4b7a-a32c-2a2b6b9a178c%2F7e6d97dc-ff19-41d4-93f3-e053c35cbd89%2Fz3pswz8_processed.png&w=3840&q=75)
Transcribed Image Text:### Probability Distributions and Calculations
**Problem Statement:**
1. **Suppose** random variable \( X \sim \mathcal{N}(2,4) \) (normal distribution with mean 2 and variance 4).
Suppose random variable \( Y \) follows the distribution below (0 and 1 are the only two possible outcomes for \( Y \)):
\[
\Pr(Y = y) =
\begin{cases}
0.4 & \text{if } y = 0 \\
0.6 & \text{if } y = 1
\end{cases}
\]
What is \( \Pr(X=1) \) and \( \Pr(Y=1) \) respectively?
**Explanation:**
- **\( X \) Distribution:**
\( X \) is normally distributed with a mean (\( \mu \)) of 2 and a variance (\( \sigma^2 \)) of 4. This distribution, denoted as \( \mathcal{N}(2,4) \), tells us about the spread and central tendency of \( X \).
- **\( Y \) Distribution:**
\( Y \) is a discrete random variable with two possible outcomes: 0 and 1. The probability distribution for \( Y \) is clearly specified:
- \(\Pr(Y = 0) = 0.4\)
- \(\Pr(Y = 1) = 0.6\)
**Questions:**
- **\( \Pr(X = 1) \):**
The question asks for the probability that the normally distributed variable \( X \) equals 1. Since the normal distribution is continuous, \(\Pr(X = 1)\) is technically zero because continuous distributions measure the probability of intervals rather than exact values.
- **\( \Pr(Y = 1) \):**
According to the provided distribution, \(\Pr(Y = 1) = 0.6\).
This problem examines understanding of both continuous and discrete probability distributions.
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