159. It is known that 10% of all radio lamps are non-standard. Find the probability that there will be no more than 1 non-standard lamp among 4 randomly taken radio lamps. 0,6561

160. 8 buyers came in a shop. What is the probability that 3 of them will do shopping if the probability to make purchase for each buyer is equal to 0,3? 0,254

161. Distribution of a discrete random variable X is given by the table

X	-2	-1	0	1
Р	1/4	¼	¼	1/4

Find the mathematical expectation M(X). -0,5

162. Distribution of a discrete random variable X is given by the table

X	-2	-1	0	1
Р	1/4	¼	¼	1/4

Find the dispersion D(X). 0,25

163. We say that a discrete random variable X is distributed under a binomial law if P(X=K) =

164. We say that a discrete random variable X is distributed under Poisson law with parameter  if

165. We say that a discrete random variable X is distributed under a geometrical law if pq^n-1

166. Dispersion of a discrete random variable X is M(X^2)-[M(X)]^2 or M(X-M(X))^2

167. Dispersion of a constant c is 0

168. The law of distribution of a discrete random variable X is given. Find Y.

	-1	2	3
	0.2	0.5	Y

169. The law of distribution of a discrete random variable X is given, M (X) = 6. Find x₁. 2

	x1	7	8
	0.3	p2	0.5

170. Distribution of a discrete random variable X is given. What is M(X) equal to? 3,9

	3	5	4
	0.4	0.3	0.3

171. A discrete random variable X is given by the law of distribution:

X	-5	0	5
P	0,2	0,6	0,2

Then the mathematical expectation M(X) is equal to: 0

172. A discrete random variable X is given by the law of distribution:

X	x1	x2	x3	x4
Р	0,2	0,1	р3	0.4

Then the probability р₃ is equal to: 0,3

173. Mathematical expectation of a normally distributed random variable X is 3, and mean square deviation is 2. Write the density of distribution X. f(x) = 1/2√2П*e^-(x-3)^2/8

174. Pairwise incompatible events A₁, A₂ and A₃ form a complete group, and P(A₁) = 0,3; P(A₃) = 0,4. Then P(A₂) is equal to: 0,3

175. For an event - landing two heads at tossing two coins - the opposite event is: at least one tail

176. A random variable X(– , ) has a normal density of distribution .

Find the value of parameter . 2

177. Show the Bernoulli formula

178. Show the mathematical expectation of a discrete random variable X: M(X) = Zxipi

179. An improper integral of density of distribution in limits from –  till  is equal to integral ot minus besk do plus besk φ (x)dx=1

180. Mathematical expectation of a continuous random variable X of which possible values belong to the entire axis OX is determined by the equality M(x) = integral ot minus besk do plus besk x φ(x)dx

181. Dispersion of a continuous random variable X of which possible values belong to the entire axis OX is defined by the equality

D(X) = integral ot minus besk do plus besk (x-a)^2 φ(x)

182. The random variable X is given by an integral function of distribution:

Find the probability of hit of the random variable X in the interval (0; 1): 1/3

183. Show one of true properties of mathematical expectation (C is a constant) M( C ) = C

184. Let M(X) = 2. Find M(X – 2). 0

185. Let M(X) = 2. Find M(2X). 4

186. Let D(X) = 2. Then D(X – 2) is equal to 2

187. Let D(X) = 3. Then D(2X) is equal to 12

188. Let f(x) be a density of distribution of a continuous random variable X. Then the function of distribution is:

F(X) = integral ot minus besk do x f(t)dt

189. Mean square deviation of a random variable X is determined by the following formula √Ds

190. A discrete random variable X is given by the law of distribution:

X	x1	x2	x3	x4
Р	р1	0,2	0,1	0,5

Then the probability р₁ is equal to: 0,2