The distribution of the binomial random variable (X) has the following parameters p = 0.3 and n = 9. Determine.
0.7052
0.9060
0.7715
0.8550
0.6255
To determine the probability mass function of X, we use the formula P(X = k) = (n choose k) * p^k * (1-p)^(n-k), where (n choose k) is the binomial coefficient or combination of n and k.
For X = 0, we have P(X = 0) = (9 choose 0) * 0.3^0 * 0.7^9 = 1 * 1 * 0.7^9 = 0.0315
For X = 1, we have P(X = 1) = (9 choose 1) * 0.3^1 * 0.7^8 = 9 * 0.3 * 0.7^8 = 0.1407
For X = 2, we have P(X = 2) = (9 choose 2) * 0.3^2 * 0.7^7 = 36 * 0.09 * 0.7^7 = 0.2335
For X = 3, we have P(X = 3) = (9 choose 3) * 0.3^3 * 0.7^6 = 84 * 0.027 * 0.7^6 = 0.2508
For X = 4, we have P(X = 4) = (9 choose 4) * 0.3^4 * 0.7^5 = 126 * 0.0081 * 0.7^5 = 0.1877
For X = 5, we have P(X = 5) = (9 choose 5) * 0.3^5 * 0.7^4 = 126 * 0.00243 * 0.7^4 = 0.0939
For X = 6, we have P(X = 6) = (9 choose 6) * 0.3^6 * 0.7^3 = 84 * 0.000729 * 0.7^3 = 0.0317
For X = 7, we have P(X = 7) = (9 choose 7) * 0.3^7 * 0.7^2 = 36 * 0.0002187 * 0.7^2 = 0.0082
For X = 8, we have P(X = 8) = (9 choose 8) * 0.3^8 * 0.7^1 = 9 * 0.0006561 * 0.7 = 0.0018
For X = 9, we have P(X = 9) = (9 choose 9) * 0.3^9 * 0.7^0 = 1 * 0.00019683 * 1 = 0.0002
Adding these probabilities together, we get 0.7052.
Therefore, the correct answer is 0.7052.