Question 1180780: Variant 1
1. A die is tossed. What is the probability that the die lands on 2? What is the probability that the die lands on a number greater than 3?
2. A student after lectures at a university can come back home either by a trolleybus or by a tram. He goes differently: he chooses a trolleybus for 2/5 cases and a tram for 3/5 cases. If he goes by a trolleybus, he comes back home to four o'clock in the afternoon in 70 % of cases, and if he goes by a tram, he comes back - only in 65 % of cases. What is the probability that he will come back home by four o'clock for a randomly taken day?
3. A standard production makes on the average 97% at some factory. A randomly selected batch of products consisting of 200 units is checked. If 7 or more non-standard products will be among them, the batch is rejected. Find the probability that: a) there will be 4 non-standard products in the batch; b) the batch of products will be accepted.
4. Discrete independent random variables X and Y are given by the following laws of distribution:
X 0 3 Y - 2 - 1 2
P 0,3 0,7 P 0,2 0,4 0,4
Find M (X + Y) by two ways: 1) composing the law of distribution of X + Y; 2) using the property: M (X + Y) = M (X) + M (Y).
5. The density of distribution of a continuous random variable X is given:
Find: a) the distribution function F(x); b) the probability of hit of the random variable X into the interval (2,5; 7).
6. A chemist is making a weighing a certain chemical substance without regular mistakes. Random errors of weighing are subordinated to a normal law with dispersion equal 225. Find the probability that a weighing will be made with a mistake which is not exceeding 5 by absolute value (weighing - взвешивание; substance - вещество).
7. The probability of occurrence of a certain event is equal to 0,6 in each of independent trials. 1000 trials have been made. Find the probability that the relative frequency of occurrence of the event deviates from its probability less than on 0,05.
8. The following data on contents of copper in ore (in grammes per one kg of ore) have been obtained after inspecting 80 samples (ore - руда):
487 324 755 651 268 162 278 845 749 577
546 445 735 754 169 243 656 812 837 569
632 536 666 577 455 361 569 754 471 751
551 669 558 122 352 457 828 643 425 652
448 839 663 142 779 446 465 642 163 755
673 849 369 252 666 778 347 848 102 452
759 335 349 264 846 675 374 796 232 817
792 394 453 365 567 358 213 377 475 166
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.
Answer by ikleyn(52809)   (Show Source):
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