Statistics and Probability Answers

. Let B be the number of boys in a family of 4 children. Construct a probability distribution of the random variable x. Construct a probability histogram 

Self Assessment/ student activity

1. A continuous random variable X that can assume values between x =

1 and x = 3 has a density function given by f (x) = 1/2. (a) Show that the

area under the curve is equal to 1. (b) Find P (2 <X < 2.5). (c) Find P

(X ≤ 1.6)

2. A continuous random variable X that can assume values between x = 2

and x = 5 has a density function given by f (x) = 2(1 +x)/27.

Find (a) P(X < 4); (b) P (3 ≤ X < 4)

3. From a box containing 4 dimes and 2 nickels, 3 coins are selected at

random without replacement. Find the probability distribution for the total

T of the 3 coins. Express the probability distribution graphi- cally as a

probability histogram.

4. From a box containing 4 black balls and 2 green balls, 3 balls are drawn in

succession, each ball being replaced in the box before the next draw is made.

Find the probability distribution for the number of green balls.

Self Assessment/ student activity

1. A continuous random variable X that can assume values between x =

1 and x = 3 has a density function given by f (x) = 1/2. (a) Show that the

area under the curve is equal to 1. (b) Find P (2 <X < 2.5). (c) Find P

(X ≤ 1.6)

2. A continuous random variable X that can assume values between x = 2

and x = 5 has a density function given by f (x) = 2(1 +x)/27.

Find (a) P(X < 4); (b) P (3 ≤ X < 4)

3. From a box containing 4 dimes and 2 nickels, 3 coins are selected at

random without replacement. Find the probability distribution for the total

T of the 3 coins. Express the probability distribution graphi- cally as a

probability histogram.

4. From a box containing 4 black balls and 2 green balls, 3 balls are drawn in

succession, each ball being replaced in the box before the next draw is made.

Find the probability distribution for the number of green balls.

Find the mean of the probability distribution of a random variable X which if 𝑃(𝑋) =

𝑥+1

20

for X= 1, 2, 3, 4, and 5.

Find the mean of the probability distribution of a random variable X which if

P(X)=1/10 for X=1, 2, 3, …, 10.

Find the mean of the probability distribution of a random variable X which can take

only the values 2, 4, 5, and 9, given that P(2)=9/20, P(5)=1/20, P(5)=1/5, and

P(9)=3/10.

Find the mean of the probability distribution of a random variable X which can take

only the values 3, 5, and 7, given that P(3)=7/30, P(5)= 1/3, and P(7)=13/30

Find the mean of the probability distribution of a random variable X which can take

only the values 1, 2, and 3, given that P(1)=10/33, P(2)= 1/3, and P(3)=1/33

Suppose that in a casino, a certain slot machine pays out an average of Php 15, with a standard deviation of Php 5,000. Every play of the game costs a gambler Php 20.

a. Why is the standard deviation so large?

b. If your parent decides to play with this slot machine 5 times, what are the mean and standard deviation of the casino's profit?

c. If the gamblers play with this slot machine 1000 times in a day, what are the mean and standard deviation of the casino's profits?

Can you make use of the normal curve to find for the probability of a large value? How?