Question

he number of different mammal species observed along a transect through a forest is a random variable X with CDF 0.01, i = 0 0.16, i = 2 0.36, i = 6 F = 0.71, i = 10 0.96, i = 18 1 i =23 What is the expected value of the random variable X?

Answer 1

The expected value of the random variable X is 6.88.

Step-by-step explanation:

The expected value of a random variable is calculated by multiplying each possible value by its corresponding probability, and then summing up these products. In this case, the possible values of X are 0, 2, 6, 10, and 18, with corresponding probabilities of 0.01, 0.16, 0.36, 0.25, and 0.05 respectively.

So, the expected value of X can be calculated as follows:

E(X) = (0 * 0.01) + (2 * 0.16) + (6 * 0.36) + (10 * 0.25) + (18 * 0.05) = 0 + 0.32 + 2.16 + 2.5 + 0.9 = 6.88

Therefore, the expected value of the random variable X is 6.88.