137. Indicate the function that can be cdf of some random variable.

• 

• 

• 

• 

• None of these

138. Indicate the function that can be pdf of some random variable.

• 

• 

• 

• 

• 

139. Continuous random variable X has the following CDF:

. What is the PDF of X in the interval 1<X≤2?

• 1/2

• 0

• 1

• X²/4

• x

140. Continuous random variable X is given in the interval [0, 100]. What is the probability P(X=50)?

• 0

• 1

• 0.5

• 0.75

• 0.25

141. CDF of discrete random variable X is given by

What is the probability P{1.3<X≤2.3}?

• 0.8

• 0.2

• 0

• 0.6

• 0.4

142. PMF of discrete random variable is given by

Х	0	2	4
Р	0,1	0,5	0,4

Find the value of CDF of X in the interval (2, 4].

• 0.4

• 0.5

• 0.2

• 0.6

• 1

143. PMF of discrete random variable is given by

Х	0	2	4
Р	0,3	0,1	0,6

Find F(2).

• 0.4

• 0.6

• 0.3

• 0.7

• 0.1

144. PMF of discrete random variable X is given by

Х	-1	5
Р	0,4	0,6

Find standard deviation of X.

• 15.4

• 8.64

• 2.6

• 2.9393

• 3.3333

145. PMF of discrete random variable X is given by

Х	-1	5
Р	0,4	0,6

Find variance of X.

• 15.4

• 8.64

• 2.6

• 2.93

• 3.33

146. PMF of discrete random variable X is given by

Х	0	5
Р	0,6	0,1	0,3

If E[X]=3.5 then find the value of x₃.

• 10

• 6

• 8

• 12

• 24

147. Probability of success in each of 100 independent trials is constant and equals to 0.8. What is the probability that the number of successes is between 60 and 88?

• 

• 

• 

• 

• 

148. A man is made 10 shots on the target. Assume that the probability of hitting the target in one shot is 0,7. What is the most probable number of hits?

• 8

• 7

• 6

• 5

• 9

149. Consider two boxes, one containing 4 white and 6 black balls and the other - 8 white and 2 black balls. A box is selected at random, and a ball is drawn at random from the selected box. If the ball occurs to be white, what is the probability that the first box was selected?

• 0.4

• 0.6

• 0.8

• 1/3

• 2/3

150. Each of two boxes contains 6 white and 4 black balls. A ball is drawn from 1^st box and it is replaced to the 2^nd box. Then a ball is drawn from the 2^nd box. What is the probability that this ball occurs to be white?

• 0.3

• 0.4

• 0.5

• 0.6

• 0.8

151. Consider two boxes, one containing 3 white and 7 black balls and the other – 1 white and 9 black balls. A box is selected at random, and a ball is drawn at random from the selected box. What is the probability that the ball selected is black?

• 0.8

• 0.2

• 0.4

• 1.6

• 0.9

152. Urn I contains 4 black and 6 white balls, whereas urn II contains 3 white and 7 black balls. An urn is selected at random and a ball is drawn at random from the selected urn. What is the probability that the ball is white?

• 0.45

• 0.15

• 0.4

• 0.9

• 1

153. A coin is tossed twice. Event A={ at least one Head appears}, event B={at least one Tail appears}. Find the conditional probability P(B|A).

• 2/3

• 1/3

• 1/2

• 3/4

• 0

154. A coin is tossed twice. Event A={ Head appears in the first tossing}, event B={at least one Tail appears}. Find the conditional probability P(B|A).

• 1/4

• 1/2

• 1/3

• 2/3

• 3/4

155. Probability that each shot hits a target is 0.9. Total number of shots produced to the target is 5. What is the probability that at least one shot hits the target?

• 1-0,9⁵

• 0,9⁵

• 1-50,9

• 1-0,1⁵

• 0,1⁵

• 1-50,1

156. An urn contains 1 white and 9 black balls. Three balls are drawn from the urn without replacement. What is the probability that at least one of the balls is white?

• 0.7

• 0.3

• 0.4

• 0.2

• 0.6

157. Four independent shots are made to the target. Probability of missing in the first shot is 0.5; in the second shot – 0.3; in the 3^rd – 0.2; in the 4^th – 0.1. What is the probability that the target is not hit.

• 1.1

• 0.03

• 0.275

• 0.003

• 1.01

158. Probability of successful result in the certain experiment is 3/4. Find the most probable number of successful trials, if their total number is 10.

• 6

• 7

• 8

• 5

• 10

159. Let E and F be two mutually exclusive events and P(E)=P(F)=1/3. The probability that none of them will occur is:

• No correct answer

• 

• 

• 

• 

160. Let Eand Fbe two events. If ,,and, then the conditional probability of Egiven F is:

• 

• 

• 

• 

• No correct answer

161. Given that Z is a standard normal random variable. What is the value of Z if the area to the left of Z is 0.9382?

• 1.8

• 1.54

• 2.1

• 1.77

• 3

162. At a university, 14% of students take math and computer classes, and 67% take math class. What is the probability that a student takes computer class given that the student takes math class?

• 0.81

• 0.21

• 0.53

• No correct answer

• 0.96

163. Let ,,, be the joint p.d.f. of X and Y. Find the marginal PDF of X.

• x

• x+1/2

• y+1/2

• x²+1

• x²+y²

164. If two random variables X and Y have the joint density function, , find the probability P(X+Y<1).

• 1/24

• 1/12

• 5/12

• 1/4

• 0.003