독립시행(정이가는 챗 봇)

Q. There are 12   light bulbs in the box, 3   of which are said to be defective. Now, take one out of this box, inspect it for defects, put it back in, and take out another one to examine it. If X   represents the number of defective products after repeating such inspection 6   times, what is the variance of X  ?

 

 

A. To find the variance of X, we can use the formula for the variance of a binomial distribution:

variance = n * p * (1 - p)

where n is the number of trials (in this case, the number of light bulbs we examine) and p is the probability of success (in this case, the probability that a light bulb is defective).

In this situation, we have n = 6 and p = 3/12 = 1/4. Plugging these values into the formula gives us:

variance = 6 * (1/4) * (3/4) = 3/8

Therefore, the variance of X is 3/8.

 

계산 실수는 인간만 하는 거 아니었어~!! 

어이, 봇~~ 정이가네

 

정답: 

불량일 확률은 =1/4

시행횟수 =6

이항분포 : B(6, 1/4)

분산은 =npq =6 *1/4* 3/4 = 9/8