15. Suppose that our random variable x  has pmf f(x)=cx  for x=1,2,3,4 . Determine the value of c.

To determine the value of \( c \), we need to use the property that the sum of the probabilities for a discrete random variable must equal 1. In this case, the random variable \( x \) has a probability mass function (pmf) given by \( f(x) = c \cdot x \) for \( x = 1, 2, 3, 4 \).

That is,

\[
f(x) = c \cdot x
\]

To find \( c \), we sum the probabilities over all possible values of \( x \) and set the sum equal to 1:

\[
f(1) + f(2) + f(3) + f(4) = 1
\]

Substitute \( f(x) = c \cdot x \) for each value of \( x \):

\[
c \cdot 1 + c \cdot 2 + c \cdot 3 + c \cdot 4 = 1
\]

\[
c(1 + 2 + 3 + 4) = 1
\]

\[
c(10) = 1
\]

Solve for \( c \):

\[
c = \frac{1}{10}
\]

Thus, the value of \( c \) is \( \frac{1}{10} \).

### Do you want more details or have any questions?

Here are 5 related questions to consider:
1. What is the expected value \( E(x) \) for this random variable?
2. How would you compute the variance of \( x \)?
3. If the values of \( x \) changed to \( x = 2, 4, 6, 8 \), how would you adjust the pmf and find the new \( c \)?
4. How would the pmf change if the range of \( x \) included 5 as well?
5. How would you calculate the cumulative distribution function (CDF) for this random variable?

**Tip:** Always verify that your pmf satisfies the condition that the total probability sums to 1 to ensure correctness.

15. Suppose that our random variable x has pmf f(x)=cx for x=1,2,3,4 . Determine the value of c.

Learn how to find the constant c in the probability mass function (PMF) f(x) = c * x for the random variable x, with values 1, 2, 3, and 4. This step-by-step solution covers key probability concepts, such as the sum of probabilities and the total probability theorem. Suitable for college-level students studying probability and statistics.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation