Let X denote the number of hours you study during a randomly selected school day The probability that X can take the values x. has the following form, where k is some unknown constant.`P(X=x)={0. 1 if x=0,k x if x=1 , 2k(5-x) if x=3 or 4, 0 otherwise

Explanation

To solve the problem, we need to determine the value of the constant \( k \) in the given probability distribution and then find various probabilities related to the random variable \( X \).

### Step 1: Define the Probability Distribution

The probability distribution is given as follows:

\[
P(X = x) =
...