A box contains 16 bulbs , out of which 4 bulbs are defective. Three bulbs are drawn at random from the box. Let X be the no of defective bulbs drawn . find the mean and variance of X

Asked by haroonrashidgkp | 5th Nov, 2018, 09:42: PM

Expert Answer:

Let X be the random variable represents number of defective bulbs drawn.
X can take values from 0 to 3
begin mathsize 16px style straight P left parenthesis straight X equals 0 right parenthesis equals fraction numerator straight C presuperscript 12 subscript 3 over denominator straight C presuperscript 16 subscript 3 end fraction space equals space 11 over 28 space space space space space space space space space space space space defective space bulbs space equals space 4 space and space non minus defective space bulbs space equals space 16 minus 4 equals 12

straight P left parenthesis straight X equals 1 right parenthesis equals fraction numerator straight C presuperscript 4 subscript 1 straight C presuperscript 12 subscript 2 over denominator straight C presuperscript 16 subscript 3 end fraction space equals space 33 over 70
straight P left parenthesis straight X equals 2 right parenthesis equals fraction numerator straight C presuperscript 4 subscript 2 straight C presuperscript 12 subscript 1 over denominator straight C presuperscript 16 subscript 3 end fraction space equals 9 over 70
Find space mean space and space variance. end style

Answered by Sneha shidid | 8th Nov, 2018, 12:17: PM