Question

Attempt History Current Attempt in Progress x 1 2 3 px) 0.20 0.35 0.45 Your answer is correct. (a) Use the probability function given in the table to calculate the mean of the random variable. Enter the exact answer. 2.25 e Textbook and Media Your Answer Correct Answer Your Answer Correct Answer * Your answer is incorrect. (b) Use the probability function given in the table to calculate the standard deviation of the random variable Round your answer to three decimal places. = 4.186 e Textbook and Media Hint Solution Attempts: unlimited Submit Answer

Answer 1

The mean of a random variable is found by summing the products of each value and its probability, while the standard deviation involves calculating the variance from the mean and then finding its square root.

Step-by-step explanation:

To calculate the mean or expected value of a discrete random variable, we sum the products of each value of the random variable (x) and its corresponding probability (p(x)). The equation for finding the mean (μ) is:

μ = Σ (x • p(x))

To calculate the standard deviation, we must follow these steps:

1. Find the mean using the method described above.
2. Use the formula σ = √[Σ((x - μ)² • p(x))] to calculate the variance (σ²).
3. Take the square root of the variance to get the standard deviation (σ).

Substitute the given values into these formulas to find the mean and standard deviation for the provided probability function.