Question

Let the random variable X have a discrete uniform distribution on the values (1, 3, 5, 7, and 9). 1) Determine the Probability Mass Function of X 2) Determine the expected value of X 3) Determine the variance of (3X - 4) 4) Determine the Cumulative Distribution Function of X. (as piecewise function) 5) Use the CDF to calculate the following Probabilities: - P(2 < X < 9) - P(X > 3.5) - P(X ? 8.5) - P(X ? 10)

          Let the random variable X have a discrete uniform distribution on the values (1, 3, 5, 7, and 9).
1) Determine the Probability Mass Function of X
2) Determine the expected value of X
3) Determine the variance of (3X - 4)
4) Determine the Cumulative Distribution Function of X. (as piecewise function)
5) Use the CDF to calculate the following Probabilities:
- P(2 < X < 9)
- P(X > 3.5)
- P(X ? 8.5)
- P(X ? 10)

Let the random variable X have a discrete uniform distribution on the values (1, 3, 5, 7, and 9).
1) Determine the Probability Mass Function of X
2) Determine the expected value of X
3) Determine the variance of (3X - 4)
4) Determine the Cumulative Distribution Function of X. (as piecewise function)
5) Use the CDF to calculate the following Probabilities:
- P(2 < X < 9)
- P(X > 3.5)
- P(X ? 8.5)
- P(X ? 10)

Added by Silvia R.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Kirsty Gledhill

05/22/2024

Step 1

Probability Mass Function (PMF) of X: Since X has a discrete uniform distribution with the values (1, 3, 5, 7), each value has an equal probability of occurring. Therefore, the PMF of X is: P(X = 1) = 1/4 P(X = 3) = 1/4 P(X = 5) = 1/4 P(X = 7) = 1/4 Show more…

Show all steps

Thanks for your feedback!

Let the random variable X have a discrete uniform distribution with the values (1, 3, 5, 7). Determine the Probability Mass Function of X. Determine the expected value of X. Determine the variance of (3X + 4). Determine the Cumulative Distribution Function of X (as a piecewise function). Use the CDF to calculate the following probabilities: P(2 < X < 9), P(X > 3.5), P(X < 8.5), P(2 < X < 10).