Consider a random variable X that follows a normal distribution with a mean (μ) of 50 and a standard deviation (σ) of 5. Calculate the probability that X is less than 40.

Suppose X is a random variable defined as final cost of project estimated cost of project which has a PDF as follows: [0 xa a. Determine the value of a. b. What is the probability that the final cost of a project will exceed its estimated cost by 25%? c. Determine the mean value and standard deviation of X.

Choose ALL THE CORRECT STATEMENTS in the following ones about probability distribution. i. Probability mass function indicates the probability distribution of a continuous random variable. ii. Probability mass function indicates the probability distribution of a discrete random variable. iii. The probability mass function of a discrete random variable X at a is denoted by P(X < a). iv. The probability function of a continuous random variable Y can be described by using P(Y= a).

Q1. Suppose X is a continuous random variable. Find an example of a probability density function for X giving expected value E(X) = 1 and variance V (X) = 3 if X has . . .  (a.) a uniform distribution. (b.) an exponential distribution. (c.) a normal distribution. In each case, if there is no such probability density function, explain why this is so.

Given the random variable X and its probability density function below find the standard deviation of X. Pr(X) 0.1 0.9 3.