96. In the first step, Joe draws a hand of 5 cards from a deck of 52 cards. What is the probability that Joe has exactly one ace?

• 0.2995

97. The number of clients arriving each hour at a given branch of a bank asking for a given service follows a Poisson distribution with parameter λ=3. It is assumed that arrivals at different hours are independent from each other. The probability that in a given hour at most 2 clients arrive at this specific branch of the bank is:

• 0.42319

98. Table shows the cumulative distribution function of a random variable X. Determine _.

X	1	2	3	4
F(X)	1/8	3/8	3/4	1

• 7/8

99. Table shows the cumulative distribution function of a random variable X. Determine _.

X	1	2	3	4
F(X)	1/8	3/8	3/4	1

• 0

100. Which of the following statements is always true for A and ?

• P(AA^c)=0

101. Consider the universal set U and two events A and B such that and. We know that P(A)=1/3. Find P(B).

• 2/3

102. A box contains 5 red and 4 white marbles. Two marbles are drawn successively from the box without replacement and it is noted that the second one is white. What is the probability that the first is also white?

• 3/8

103. If P(A)=1/2 and P(B)=1/2 then

• 1/4, if A and B are independent or 3/8

104. Suppose that P(A|B)=3/5, P(B)=2/7, and P(A)=1/4. Determine P(B|A).

• 24/35

105. A class contains 8 boys and 7 girls. The teacher selects 3 of the children at random and without replacement. Calculate the probability that the number of boys selected exceeds the number of girls selected.

• 28/65

106. If the variance of a random variable X is equal to 3, then Var(3x) is :

• 27

107. Let X and Y be continuous random variables with joint cumulative distribution function forand. Find P(X>2).

• 12/25

108. Indicate the correct statement related to Poisson random variable .

• ,

109. Let X be a continuous random variable with PDF f(x) = cx (0 ≤ x ≤ 1), where c is a constant. Find the value of constant c.

• 2

110. We are given the pmf of two random variables X and Y shown in the tables below.

Х	1	3			У	2	4
px	0,4	0,6			py	0,2	0,8

Find E[X+Y].

• 5.8

111. The pdf of a random variable X is given by . Calculate the parameter.

• 4

112. Four persons are to be selected from a group of 12 people, 7 of whom are women. What is the probability that three of those selected are women?

• 0.35

113. Suppose that the random variable T has the following probability distribution:

t | 0 1 2 --------------------------- P(T = t) | .5 .3 .2 Find .

• 0.8

114. Suppose that the random variable T has the following probability distribution:

t | 0 1 2 --------------------------- P(T = t) | .5 .3 .2 Compute the mean of the random variable T.

• 0.7

115. Three dice are rolled. What is the probability that the points appeared are distinct.

• 5/9

116. Probability density function of the normal random variable X is given by . What is the standard deviation?

• 5

117. The event A occurs in each of the independent trials with probability p. Find probability that event A occurs at least once in the 5 trials.

• 

118. The cdf of a random variable X is given byFind the probability P(1.7<X<1.9).

• 0,4