If a random variable x has the probability distribution array |c|c|c|c|c|c|c|c|c| x & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 P(x) & 0 & 2k & k & 3k & 2k² & 2k & k²+k & 7k² array then P(3 < x 6) is equal to

Step-by-step solution

Sum of all probabilities = 1 0 + 2k + k + 3k + 2k^2 + 2k + (k^2+k) + 7k^2 = 1 10k^2 + 9k - 1 = 0 . (10k-1)(k+1) = 0 k = 1 10 (rejecting k = -1 ). P(3 = 2k^2 + 2k + k^2 + k = 3k^2 + 3k = 3(0.01) + 3(0.1) = 0.33 .