Variant 2

1. Two shooters make shots in a target. The probability of hit in the target at one shot by the first shooter is 0,7; and by the second shooter – 0,9. Find the probability that at one shot: a) both shooters will hit in the target; b) only one of the shooters will hit in the target.

2. Two automatic devices make plastic hangers. The probability of making a non-standard hanger by the first automatic device is 0,08; and by the second – 0,1. The productivity of the first automatic device is twice more than the second. Find the probability that a randomly taken detail will be non-standard.

3. The probability that a receipt written out by a shop assistant will be paid by a buyer is equal to 0,8. The shop assistant has written out 16 receipts. Find the most probable number of paid receipts and calculate its probability (receipt – чек).

4. Two independent random variables X and Y are given by the following tables of distribution:

X	1	2		Y	1	3	4
P	0,7	0,3		P	0,5	0,3	0,2

Compose the law of distribution of their sum Z = X + Y and check the property: D(X + Y) = D(X) + D(Y).

5. The random variable X is given by the distribution function:

Find: a) the mathematical expectation and the dispersion; b) the probability of hit of the random variable X into the interval (3; 8).

6. It is supposed that the strength of a let out party of a parachute fabric is a normally distributed random variable X with the mathematical expectation a = 200 kg/cm² and the mean square deviation  = 12 kg/cm² (to let out – выпускать; parachute fabric – парашютная ткань).

Find: 1) the differential function of distribution f(x) and the integral function of distribution F(x); 2) the probability that X will take on a value from 175 up to 225 kg/cm².

7. A factory makes products, and 80% of them are the first grade. Estimate the probability that the part of products of the first grade among 10000 made products will differ from the probability of making a product of the first grade no more than on 0,03 by absolute value.

8. There are the following data on lifetime of a separate parachute produced by a certain factory after studying 50 samples:

227	512	405	292	630	315	424	222	377	596
318	601	132	115	518	293	488	103	294	518
402	326	305	217	298	585	312	302	418	298
603	505	292	285	422	215	518	651	503	258
195	497	612	306	192	465	142	686	320	202

1) Compose the interval and the discrete variation series taking the beginning of the first interval equal 100, and the width of each interval equal 50.

2) Construct the histogram and the polygon of relative frequencies of distribution.

3) Find the mode and the median (using the discrete series).

4) Find empirical functions of distribution of continuous and discrete variation series; and construct their graphs.