5 A sotware package consists of 9 programs, 4 of which must be upgraded. 3 programs...
Find the standard deviation of Pandoi vallabie 5. A software package consists of 9 programs, 4 of which must be upgraded. 3 programs are randomly chosen for testing. Construct the distribution law for the number of programs that must be upgraded among chosen.
Find the distribution law oi te a 6. A software package consists of 11 programs, 7 of which must be upgraded. 5 programs are needn't be upgraded among chosen. randomy chosen for testing. Construct the distribution law for the number of programs that bilitu donsity function:
7. Let X be a continuous random variable whose probability density function is: 2x3 +ax2, if x (0; 1) if x (0;1) 0, Find 1) the coefficient a; 2) P(O.5ex<0.7):3) P(X>3). wness, Part 3. Statistics A sample of measurements is given 8. Compute the coefficient of correlation, make conclusions about dependence of variables. 9. Find the line of the linear regression of Y from X and draw it on the scatter plot.
Find the variance of random variable X. 7.. Let X be a continuous random variable whose probability density function is: -(2x3 + ar', if x E (0:1) if x (0;1) Find 1) the coefficient a; 2) P(O.5eX<0.7); 3) P(X>3). Part 3. Statistics A sample of measurements is given X 8 -2 0 2 8
1. Two independent random variables X and y are given with their distribution laws 4 P 07 0.1 0.2 P 0.2 0.3 0.5 Find 1) the variance of random variable Y 2) the distribution law of random variable Z-0.5Y+x END TEST IN PROBABL ITY THEORY AND STAISTICS Variant 1 1. Two independent random vanables X and Y are given with their distribution laws: 2 0.7 0.1 P 0.2 0.3 0.5 0.2 Find 1) the variance of random varñable Y 2)...
2ND TEST IN PROBABILITY THEORY AND STATISTICS Variant 8 1. X is a continuous random variable with the cumulative distribution function if x<0 F(x)ax2 0.1x if osxs 20 if x> 20 0 Find 1) the coefficient a; 2) P 10); 3) P(X<30). 2. The result of some measurement X is normally distributed with parameters 184 and 8. Compute the probability that variable X takes value from interval (170;180) at least once in 5 experiments 3. Two independent random variables X...
0.54. Find the probablty a 5. Two independent random variables X and y are given with their distribution laws Xi 0.5 1 Pi 0.2 0.8 Yi 2 0| 2 Pi 0.3 0.4 0.3 Find the distribution law of the random variable W 4X-Y. fuhich must be upgraded. 5 programs are
Part 2. Random Variables 4. Two independent random variables Xand y are given with their distribution laws 0.3 0.7 0.8 0.2 Pi Find the distribution law and variance for the random variable V-3XY 5. There are 7 white balls and 3 red balls in a box. Balls are taken from the box without return at randomm until one white ball is taken. Construct the distribution law for the number of taken balls. 6. Let X be a continuous random variable...
6th
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robability Theory and Mathematical statistics Final examination Variant 4 Part 1. Random Events he probability that a computer crashes during a severe thunderstorm is 0.005. A certain npany had 550 working computers when the area was hit by a severe thunderstorm. Compute ne probability that exactly 2 computers crashed. 2. It is known about random events A and B that PCB) = 5P (AB). PCA) = 0.7and P(A + B) = 0.6. Find P(B). 3....