The probability distribution of a random variable X is given by: x 12 3 4 P(X) k 2k 3k | 4k (a) Find the value of the constant k. (b) Two successive values of X are generated independently of each other. Find the prob- ability that the total of the two values of X is greater than 6. (b)
The probability distribution of a random variable X is given by: x 12 3 4 P(X) k 2k 3k | 4k (a) Find the value of the constant k. (b) Two successive values of X are generated independently of each other. Find the prob- ability that the total of the two values of X is greater than 6. (b)
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 Distribution Problem**
The probability distribution of a random variable \( X \) is given by the table below:
\[
\begin{array}{|c|c|c|c|c|}
\hline
X & 1 & 2 & 3 & 4 \\
\hline
P(X) & k & 2k & 3k & 4k \\
\hline
\end{array}
\]
**Tasks:**
(a) **Find the value of the constant \( k \).**
*Answer (a):* __________
(b) Two successive values of \( X \) are generated *independently of each other*. Find the probability that the total of the two values of \( X \) is greater than 6.
*Answer (b):* __________
**Explanations:**
- **Table Description:**
- The table represents a probability distribution of a discrete random variable \( X \) with possible values 1, 2, 3, and 4.
- The probabilities \( P(X) \) corresponding to these values are expressed in terms of a constant \( k \): \( k, 2k, 3k, \) and \( 4k \).
- **Probability Calculation:**
- To find \( k \), note that the sum of probabilities must equal 1: \( k + 2k + 3k + 4k = 1 \).
- **Independent Events:**
- For part (b), since the two values of \( X \) are independent, their combined probabilities can be calculated using the laws of probability for independent events.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fab8e90de-1834-4897-8d02-45bfaff51002%2Fa222dfaa-d3d8-44bb-b1b4-6c9b4d98c161%2F8hbpduh_processed.png&w=3840&q=75)
Transcribed Image Text:**Probability Distribution Problem**
The probability distribution of a random variable \( X \) is given by the table below:
\[
\begin{array}{|c|c|c|c|c|}
\hline
X & 1 & 2 & 3 & 4 \\
\hline
P(X) & k & 2k & 3k & 4k \\
\hline
\end{array}
\]
**Tasks:**
(a) **Find the value of the constant \( k \).**
*Answer (a):* __________
(b) Two successive values of \( X \) are generated *independently of each other*. Find the probability that the total of the two values of \( X \) is greater than 6.
*Answer (b):* __________
**Explanations:**
- **Table Description:**
- The table represents a probability distribution of a discrete random variable \( X \) with possible values 1, 2, 3, and 4.
- The probabilities \( P(X) \) corresponding to these values are expressed in terms of a constant \( k \): \( k, 2k, 3k, \) and \( 4k \).
- **Probability Calculation:**
- To find \( k \), note that the sum of probabilities must equal 1: \( k + 2k + 3k + 4k = 1 \).
- **Independent Events:**
- For part (b), since the two values of \( X \) are independent, their combined probabilities can be calculated using the laws of probability for independent events.
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