Question

Let X be a continuous random variable with the following PDF:

fX (x) ={ x⁹(12x²+11x−10) 0{0 otherwise
Find the value of 98E[X].Enter your answer correct to two decimals accuracy.

Answer 1

To find the value of 98E[X], we need to calculate the expected value of the continuous random variable X using its probability density function (PDF). This involves integrating the product of x and fX(x) over its range of values.

Step-by-step explanation:

To find the value of 98E[X], we need to calculate the expected value of the random variable X. The expected value, denoted by E[X], is calculated by multiplying each value of X by its corresponding probability and summing them up. In this case, we have a continuous random variable with a probability density function (PDF) given by fX(x) = x^9(12x^2 + 11x - 10). To calculate E[X], we integrate the product of x and fX(x) over its entire range of values.

E[X] = ∫-∞+∞ x*fX(x) dx

Once we have the integral, we can evaluate it to find the expected value of X. Since the question asks for the value of 98E[X], we need to multiply the result of E[X] by 98.