Discrete and Continuous Type Random Variables
Consider a discrete random variable X with the following PMF:
P(X = 1) = 0.3, P(X = 2) = 0.5, P(X = 3) = 0.2.
Calculate the variance of the random variable X.
A continuous random variable Y follows a uniform distribution between 0 and 10. Calculate the probability that Y is between 2 and 6.
The expected value of a discrete random variable Z is 3. If Z has distribution function P(Z = 1)=0, P(Z = 2)=p1, P(Z = 4)=p2, P(Z = 5) = 0. what is the probability of Z being equal to 4?
Let W be a continuous random variable with a normal distribution having a mean of 50 and a standard deviation of 10. What is the probability that W is less than 45?
A Poisson-distributed random variable X represents the number of emails received per hour, with an average rate of 5 emails per hour. What is the probability of receiving exactly 3 emails in a given hour?