Let X denote the number of hours you study on a Sunday. It is known that. P ( X = x )= array cl 0 1 & , if x=0 k x & , if x=1 or 2 k (5-x) & , if x=3 or 4 0 & , otherwise array . where k is constant. Then the probability that you study at least two hours on a Sunday is

Step-by-step solution

The probability that at least two hours are studied on Sunday is given by P(X 2) = P(X=2) + P(X=3) + P(X=4) . The constant k in the probability mass function is determined by the condition that the sum of probabilities must equal 1. The probabilities are P(X=0) = 0.1 , P(X=1) = k , P(X=2) = 2k , P(X=3) = 2k , P(X=4) = k . Summing these gives 0.1 + k + 2k + 2k + k = 0.1 + 6k = 1 . Solving for k , 6k = 0.9 , so k = 0.15 . Substituting k = 0.15 yields P(X=2) = 0.30 , P(X=3) = 0.30 , and P(X=4) = 0.15 . The total proba