119. In each of the 20 independent trials the probability of success is 0.2. Find the variance of the number of successes in these trials.

• 3.2

120. A coin tossed twice. What is the probability that head appears in the both tosses.

• 1/4

121. Continuous random variable X is normally distributed with mean=1 and variance=4. Find P(4≤x≤6).

• 0,0606

122. Random variable X is uniformly distributed on the interval [-2, 2]. Indicate the right values for E[X] and Var(X).

• E[X]=0 and Var(X)=1.33

123. Expectation and standard deviation of the normally distributed random variable X are respectively equal to 15 and 5. What is the probability that in the result of an experiment X takes on the value in interval (5, 20)?

• (1) + (2)-1

124. Normally distributed random variable X is given by density . Find the mean.

• 0

125. Indicate the density function of the normally distributed random variable X when mean=2 and variance=9.

• 

126. Indicate the pdf for standard normal random variable.

• 

127. Random variable X is uniformly distributed in interval [0, 3]. What is the variance of X?

• 0.75

128. Random variable X is uniformly distributed in interval [0, 15]. What is the expectation of X?

• 7.5

129. Random variable X is uniformly distributed in interval [-2, 1]. What is the distribution of the random variable Y=2X+2?

• Y is uniformly distributed in the interval [-2, 4]

130. Random variable X is uniformly distributed in interval [-11, 26]. What is the probability P(X> - 4)?

• 30/37

131. Random variable X is uniformly distributed in interval [1, 3]. What is the distribution of the random variable Y=3X+1?

• Y is uniformly distributed in the interval [4, 10]

132. Random variable X is uniformly distributed in interval [-11, 20]. What is the probability P(X ≤ 0) ?

• 11/31

133. Random variable X is given by density function f(x) in the interval (0, 1) and otherwise is 0. What is the expectation of X?

• 

134. Random variable X is given by density function f(x) = x/2 in the interval (0, 2) and otherwise is 0. What is the expectation of X?

• 4/3

135. Random variable X is given by density function f(x) = 2x in the interval (0, 1) and otherwise is 0. What is the expectation of X?

• 2/3

136. Random variable X is given by density function f(x) = 2x in the interval (0, 1) and otherwise is 0. What is the probability P(0 < X < 1/2) ?

• 1/4

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

• 

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

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

• 0

141. CDF of discrete random variable X is given by

What is the probability P{1.3<X≤2.3}?

• 0.2

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].

• 0.6

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

144. PMF of discrete random variable X is given by

Х	-1	5
Р	0,4	0,6

Find standard deviation of X.

• 2.9393

145. PMF of discrete random variable X is given by

Х	-1	5
Р	0,4	0,6

Find variance of X.

• 8.64

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

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?

• 7

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?

• 1/3

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?

• 0.6

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

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

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

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).

• 1/2

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?

• 1-0,1⁵

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?

• 0.3

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.

• 0.003

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.

• 8

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:

• 

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

• 

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?

• 1.54

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?

• 0.21

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

• x+1/2

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

• 1/24