Probability theory and mathematical statistics

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1. The telephone number consists of 6 digits. What is the probability that all the figures in it: a) is different; b) the same; c) the odd? It is known the phone number does not begin with a numeral zero.

2. To put the lead four roads. Likely to die on the first road is 0.2, the second - 0.4, on the third - 0.2, on the fourth - 0.4. Find the probability that the treasure hunter gets to the treasure, if the road is chosen fail.

3. There is an opportunity to invest in the shares of one of the three companies. The probability that the shares of the first company within the month will fall, is 0.5, the second - 0.3, the third - 0.7. It is known that the purchased shares fell in price. What is the probability that it was the first action of the enterprise, if the question is: "The shares of the company to buy?" Hesitated at random.

4. Hunter, with 5 rounds in the game to shoot the first hit. The probability of hitting the first shot is 0.7 and decreases with every shot 0.1. Create the distribution law of the spent ammunition. Find M (X), D (X), σ (X) and F (X) of the spent ammunition.

5.Dana distribution function of the random variable X

6. Dana density distribution of a continuous random variable X. Find: a) setting a; b) the distribution function F (X).

 7.Sdaetsya 240-apartment building. The probability that a single apartment building deficiencies are found, to be 0.3. Find the probability that the deficiencies will be found no more than 30 apartments.

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