Write the values of ‘a’ for which the following distribution of probabilities becomes a probability distribution:

Two numbers are selected at random (without replacement) from positive integers 2,3,4,5,6 and 7. Let X denote the larger of the two numbers obtained. Find the mean and variance of the probability distribution of X.

In a game, a man wins ₹5 for getting a number greater than 4 and loses ₹1 otherwise, when a fair die is thrown. The man decided to throw a die thrice but to quits as and when he gets a number than 4. Find the expected value of amount he wins/lose.

For what value of k the following distribution is a probability distribution?

If X denotes the number on the upper face of a cubical die when it is thrown, find the mean of X