Please help Thank you Identify the following random variables as discrete or con

Question

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Identify the following random variables as discrete or continuous: N, the number of traffic accidents in a day in Delaware. P, the number of pizzas ordered by UD students in a day. T, the time between ordering a pizza and its delivery. C, the crushing strength of concrete. W, the concentration of atmospheric SO_2 at 10 am in Newark. S, the SAT score of a high school student applying to UD. (b) Two events A and B are such that P(A Union B) = 0.5, P(A)= 0.3, P(B)=0.25. Are A and B disjoint?

Explanation / Answer

1(a)

A discrete variable is a variable whose value is obtained by counting.

A continuous variable is a variable whose value is obtained by measuring.

N) The number of traffic accedents in a day in delaware is obtained by counting hence it is a Discrete random variable

P) The number of pizzas ordered by UD students in a day is obtained by counting it is a Discrete random variable

T) the time between ordering pizza and its delivery is obatained by measuring it is a Continuous random variable

C) The crushing strength of concrete is obatained by measuring so it is a Continuous random variable

W) the concentration of atmospheric so2 at 10 am in newark it is obtained by measuring hence it is a Contiuous random variable

S) The SAT score of high school student applying UD is obatained by counting hence it is a Discrete random variable

1b)

If the events are disjoint, then P(A B)=0

p(AUB) = P(A) + P(B)

for the given value P(A) = 0.3

P(B) = 0.25

P(A) + P(B) = 0.3+0.25 = 0.55 which is not equal to p(AUB) hence the two events are not disjoint

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