suppose a random variable x is best described by a uniform probability distribut

Question

suppose a random variable x is best described by a uniform probability distribution with range 2 to 5. Find the value of a that makes the following probability statements true.

(a) P(xa)=0.24   A=?

(b) P(x>a)=0.41 A=?

(c) P(2.29xa)=0.36 A=?

PART B

In a certain community, the probability that a family owns a dog is 35%. Given that a family owns a dog, the probability that they also own a cat is 20%. It is also known that 32% of all the families own a cat.
What is the probability that a randomly selected family owns a dog?

What is the conditional probability that a randomly selected family owns a dog given that it owns a cat?

Hint: Write out each of the probabilities you've been given in probability notation, as well as the probabilities you need to find. You may need to find a joint probability ( P(A and B)) before you can answer the 2nd question. It may help to draw a Venn Diagram. Be sure to give your answers to at least 4 decimal places.

Explanation / Answer

a) P(X<a) =0.24

(a-2)/(5-2) =0.24

a =2+0.24*3=2.72

b) P(X>a) =0.41

(5-a)/(5-2)=0.41

5-a =1.23

a =3.77

c) P(2.29<x<a) =0.36

(a-2.29)/(5-3) =0.36

a-2.29 =1.08

a =3.37

b)

(i)here probability that a randomly selected family owns a dog P(dog) =0.35

(ii) also P(cat) =0.32

P(cat|dog) =0.20

hence  conditional probability that a randomly selected family owns a dog given that it owns a cat

=P(Dog|cat) =P(dog)*P(cat|dog)/P(cat) =0.35*0.20/0.32=0.21875

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