Let X be a random variable with density functionfX (x) = k1 + x2 , −∞ < x < ∞.Determine k and the distribution function

Question

Let X be a random variable with density functionfX (x) = k1 + x2 , −∞ < x < ∞.Determine k and the distribution function
🧐 Not the exact question you are looking for?Go ask a question

Solution 1

To find the value of k such that the function f is a probability density function, we need to ensure that the integral of f from -∞ to ∞ is equal to 1, because the total probability must be 1.

The function f is non-zero for all real numbers, so we need to integrate from -∞ to ∞:

∫ from -∞ to ∞ of Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob

Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solv

This problem has been solved

Similar Questions

Let X be a random variable with density functionfX (x) = k1 + x2 , −∞ < x < ∞.Determine k and the distribution function

Let X be a random variable with probability mass functionx -3 6 9pX (x) 1/6 1/2 1/3Find E(X), E(X2) and E(2X + 1)2

Which property of the moment generating function allows us to uniquely determine the distribution of a random variable?

Suppose the cumulative distribution function of a random variable X is given by :Calculate P(1 < X < 3)?

3. Let random variable X has exponential distribution with parameter ν.Find probabilityP (X ∈ [E(X) − σX ; E(X) + σX ])where σX is standard deviation of X.

1/3