True or false With explanations please For the events A and

For the events A and B. (A\'IntersectionB)IntersectionA - Oslash The probability of the union of two events is never larger than the sum of the individual probabilities of the events. If A and B are mutually exclusive, then A\' and B\' are independent. If C has a Chi-square distribution with (n-1) degrees of freedom, then E[C ]=n. Let P be some proportional random variable. The Central Limit Theorem tells us that as tlie sample size or n increases, the distribution of P is approximately normal.

Solution

2) the question says P(AUB) IS NEVER LARGER THEN THE INDIVIDUAL SUM OF PROBABILITIES

AS P(AUB) = P(A)+P(B) - P(A INTERSECTION B)

EVEN IS WE CONSIDER THE PART OF INTERSECTION IS 0 THEN ALSO P(AUB) WILL BE EQUAL TO P(A)+P(B)

HENCE IT CAN NEVER BE BIGGER THEN P(B)+P(A)

HENCE THIS IS TRUE.