165. If two random variables X and y have the joint density function, , find the conditional pdf.

• 

• 

• 

• 

• None of these

166. If two random variables X and y have the joint density function, , find the conditional pdf.

• 

• 

• 

• 

• None of these

167. A basketball player makes 90% of her free throws. What is the probability that she will miss for the first time on the seventh shot?

• 0.0001

• 0.053

• 0.002

• 0.001

• 0.01

168. The joint distribution for two random variables X and Y is given by . Then find P(Y>0.5).

• 0.5

• 0.25

• 0.75

• 1

• 1.5

169. Let X be a continuous random variable with probability density given by . Let Y=2X-3. Find P(Y≥4).

• 0.3438

• 0.53125

• 0.0625

• 0.1563

• 0

170. Random variable X has the following PDF

Find .

• 0.31

• 0.428

• 0.512

• 0

• 0.78

171. Random variable X has the following PDF

Find E[X].

• 0

• 1

• 2

• 3

• 4

172. Random variable X has the following PDF

Find Var[X].

• 0

• 1

• 0.6

• 0.8

• 0.4

173. Random variable X has the following PDF

Find .

• 4

• 0

• 2

• 1

• -2

174. The joint distribution for two random variables X and Y is given by . Find the marginal density function for X.

• 6y

• 6y²

• 6x²

• 3x²

• 3x³

175. The joint distribution for two random variables X and Y is given by . Find the marginal density function for Y.

• 3x²

• 6y

• 2y

• 2y²-1

• y+6

176. The joint distribution for two random variables X and Y is given by . Find the E[X].

• 0.25

• 0.75

• 0.5

• 0.95

• None of these

177. The joint distribution for two random variables X and Y is given by . Find the E[Y].

• 1

• 2/3

• 1/3

• 0.5

• 0.25

178. Assume that Z is standard normal random variable. What is the probability P(|Z|>2.53)?

• 0.9943

• 0.0114

• 0.0057

• 0.9886

• None of these

179. If Z is normal random variable with parameters µ=0, σ²=1 then the value of c such that P(|Z|<c)=0.7994 is

• 1.28

• 0.84

• 1.65

• 2.33

• None of these

180. The random variable X has the continuous CDF

. Find P(2≤X≤4).

• 16/9

• 4/3

• 4/9

• 5/9

• 2/3

181. Let X be the random variable for the life in hours for a certain electronic device. The probability density function is

. Find the expected life for a component.

• 2000 hours

• 1000 hours

• 100 hours

• 200 hours

• None of these

182. The joint distribution for two random variables X and Y is given by . Find E[X-Y].

• 0

• 7/6

• 2/3

• 1/6

• None of these

183. The joint distribution for two random variables X and Y is given by . Find E[X+Y].

• 1/6

• 6/7

• 7/6

• 5/6

• 0

184. The joint density function for the random variables X and Y is given by . Find E[X].

• 0

• 1

• 1.4142

• 2

• None of these

185. A box contains 15 balls, 10 of which are black. If 3 balls are drawn randomly from the box, what is the probability that all of them are black?

• 0.26

• 0.52

• 0.1

• None of these

• 0.36

186. The Cov(aX,bY) is equal to

• 

• 

• 

• 

• 

187. If A and B are two mutually exclusive events with P(A) = 0.15 and P(B) = 0.4, find the probability P(A and B^c) (i.e. probability of A and B complement).

• 0.4

• 0.15

• 0.85

• 0.6

• 0.65

188. From a group of 5 men and 6 women, how many committees of size 3 are possible with two men and 1 woman if a certain man must be on the committee?

• 

• 

• 

• 

• None of these

189. Let ,,, be the joint PDF of X and Y. Find the marginal PDF of Y.

• y+1/2

• y

• 1/2y

• y²/2

• 1/2

190. Let ,,, be the joint PDF of X and Y. Compute E[X].

• 0.2

• 0.823

• 0.583

• 1

• 0

191. Let ,,, be the joint PDF of X and Y. Compute E[Y].

• 0.2

• 0.823

• 0.583

• 1

• 0

192. Let ,,, be the joint PDF of X and Y. Compute E[2X].

• 7/6

• 0

• 1

• 7/12

• 1/6

193. Let X be continuous random variable with probability density function .Find the expected value of random variable X.

• 19/3

• 13/3

• 12/7

• 28/9

• 27/4

194. The joint distribution for two random variables X and Y is given by . Then find P(X>0.5).

• 0.5

• 0.25

• 0.15

• 0.75

• 0.1

195. Probability mass function for discrete random variable X is represented by the

graph. Find Var(X).

• 1

• 4

• 5

• 2

• 6

196. Two dice are rolled, find the probability that the sum is less than 13.

• 1

• 1.2

• 0.5

• 0.6

• 0.8

197. A bag has six red marbles and six blue marbles. If two marbles are drawn randomly from the bag, what is the probability that they will both be red?

• 1/2

• 11/12

• 5/12

• 5/22

• 1/3

198. A man can hit a target once in 4 shots. If he fires 4 shots in succession, what is the probability that he will hit his target?

• 175/256

• 1

• 1/256

• 81/256

• 144/256

199. Let random variable X be normal with parameters mean=5, variance=9. Which of the following is a standard normal variable?

• Z=(X-5)/5

• Z=(X-3)/5

• Z=(X-5)/3

• Z=(X-3)/3

• None of these

Конец формы

1. A coin is tossed 6 times. What is the probability of exactly 2 heads occurring in the 6 tosses.

• 

• 

• 

• 

• None of these