There rotten apples are mixed accidently with seven good apples and four apples are drawn one by one without replacement. Let the random variable X denote the number of rotten apples. If μ and σ 2 represent mean and variance of X, respectively, then 10 μ 2 + σ 2 is equal to

Step-by-step solution

There rotten apples are mixed accidently with seven good apples, And four apples are drawn one by one without replacement. Now the random variable X denote the number of rotten apples. And μ and σ 2 represent mean and variance of X, respectively, So, now plotting the table of given data we get, x P ( x ) x P ( X ) x 2 P ( X ) 0 1 6 0 0 1 1 2 1 2 1 2 2 3 10 6 10 12 10 3 1 30 1 10 9 30 Now mean is given by, ∑ x P ( x ) = 6 2 = μ And variance is given by σ 2 = ∑ x 2 P ( x ) - μ 2 S