Probability and Stochastic Processes-Homework 4-Solution Explanation

1.P(X=k)=Ak(1/2)^(k-1),k=1,2,...,infinity.
Find A so that P(X=k) represents a probability mass function
Find E{X}
2.Find the mean and variance of a given probability density function

[annamalaigokkulnatarajan]

Thank You Sir. I will take note of these points and make the necessary changes for my next presentation

[probabilitystochasticproce]

Good presentation, although your choice of x to represent 1/2 is unfortunate because you use the same x for the random variable as well. Look at T=4.00 minute into your presentation. E(x) is in terms of x on the right side, both x look the same.

For the second part if you make a simple substitution u =x-1 within the integral, then you can use the results of standard exponential random variables. Might be easier. Less computations. What you have is brute force, that is fine too.