Based on the given random variables and the probability values, the expected value of X is 5.375.
How to compute the expected value of X
Let's compute the expected value of X using the provided probabilities for Y and the relationships between Y and X:
When Y=1 with probability of 1/8, X=1.
When Y=2 with probability of 3/4, X=2Y=4.
When Y=X with probability of 7/8, X=Y=2.
When Y=3 with probability of 1/4, X=3Y=9.
Let's calculate E[X] step by step:
The expected value E[X] is given by the sum of each outcome multiplied by its respective probability:
The expected value E[X] is calculated as follows:
E[X] = (1 * 1/8) + (4 * 3/4) + (2 * 7/8) + (9 * 1/4)
E[X] = 1/8 + 3 + 14/8 + 9/4
E[X] = 1/8 + 3 + 7/4 + 9/4
E[X] = 1/8 + 12/4 + 9/4
E[X] = 1/8 + 21/4
E[X] = (1 + 42)/8
E[X] = 43/8
E[X] = 5.375
Therefore, the expected value of X is 5.375.
Suppose random variables Y and X are distributed as below. What is E[X]? Show all steps of your work:
1 with probability 1/8,
2Y with probability 3/4,
Y = X with probability 2 with probability 7/8,
3Y with probability 1/4.