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Find the variance of random variable X. 7.. Let X be a continuous random variable whose...
7. Let X be a continuous random variable whose probability density function is: 2x3 +ax2, if...
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.
Let X be a continuous random variable whose probability density function is fax) (2x +af (0...
Let X be a continuous random variable whose probability density function is fax) (2x +af (0 1) if x E (0; 1) f (x) - ind 1) the coefficient a; 2) P(0.5<X<0.7); 3) P(X 3) Part 3 sample of measurements is given XI-8 -210|2|8 Y 8 4 2 2 0
6. The distribution law of random variable X is given -0.4 -0.2 0 0.1 0.4 0.3...
6. The distribution law of random variable X is given -0.4 -0.2 0 0.1 0.4 0.3 0.2 0.6 Xi Pi Find the variance of random variable X. 7. Let X be a continuous random variable whose probability density function is: f(x)=Ice + ax, ifXE (0,1) if x ¢ (0:1) 0, Find 1) the coefficient a; 2) P(O.5 X<0.7); 3) P(X>3). Part 3. Statistics A sample of measurements is given Y 8 4 2 2 0 8. Compute the coefficient of...
5 A sotware package consists of 9 programs, 4 of which must be upgraded. 3 programs...
5 A sotware package consists of 9 programs, 4 of which must be upgraded. 3 programs are randomiy dhosen for testing Construct the distribution law for the number of programs that must be upgraded among chosen. 6. The distribution law of random variable X is given 01 04 03 02 Find the variance of random variable X 7. Let X be a continuous random variable whose probability density function is: 2x3+ax2, ifx E (0; 1) if x (0;1) f(x) 0,...
6. Let X be a continuous random variable whose probability density function is: 0, x <0,...
6. Let X be a continuous random variable whose probability density function is: 0, x <0, x20.5 Find the median un the mode. 7. Let X be a continuous random variable whose cumulative distribution function is: F(x) = 0.1x, ja 0S$s10, Find 1) the densitv function of random variable U-12-X. 0, ja x<0, I, ja x>10.
5. Find the moment generating function of the continuous random variable X whose a. probability density...
5. Find the moment generating function of the continuous random variable X whose a. probability density is given by )-3 or 36 0 elsewhere find the values of μ and σ2. b, Let X have an exponential distribution with a mean of θ = 15 . Compute a. 6. P(10 < X <20); b. P(X>20), c. P(X>30X > 10), the variance and the moment generating function of x. d.
4. Let X be a continuous random variable with probability density function: x<1 0, if if|...
4. Let X be a continuous random variable with probability density function: x<1 0, if if| if x>4 f(x) = (x2 + 1), 4 x 24 0 Find the standard deviation of random variable X.
5. (20%) Let X be a continuous random variable whose probability density function is fr(x) (a +bx)%0(x) (a) If Ex)f...
5. (20%) Let X be a continuous random variable whose probability density function is fr(x) (a +bx)%0(x) (a) If Ex)f find a and b. (b) Give the cumulative distribution function F,(x) f()dt of X and Var(X) (c) Let A be any Borel set of R. Define P by P(A) [,f dm
5. (20%) Let X be a continuous random variable whose probability density function is fr(x) (a +bx)%0(x) (a) If Ex)f find a and b. (b) Give the cumulative distribution...
2ND TEST IN PROBABILITY THEORY AND STATISTICS Variant 8 1. X is a continuous random variable with the cumulative distri...
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...
13. Let X be a continuous random variable with density P(X0)0.3 and P(X 1) 0.7. Find...
13. Let X be a continuous random variable with density P(X0)0.3 and P(X 1) 0.7. Find (i) 1 - Fx(t) where Fx(t) is the cumulative distribution function of X (i) 1-Fx (t) da (iii) 0-P(X = 0) + 1 . P(X = 1) 0
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.
Let X be a continuous random variable whose probability density function is fax) (2x +af (0 1) if x E (0; 1) f (x) - ind 1) the coefficient a; 2) P(0.5<X<0.7); 3) P(X 3) Part 3 sample of measurements is given XI-8 -210|2|8 Y 8 4 2 2 0
6. The distribution law of random variable X is given -0.4 -0.2 0 0.1 0.4 0.3 0.2 0.6 Xi Pi Find the variance of random variable X. 7. Let X be a continuous random variable whose probability density function is: f(x)=Ice + ax, ifXE (0,1) if x ¢ (0:1) 0, Find 1) the coefficient a; 2) P(O.5 X<0.7); 3) P(X>3). Part 3. Statistics A sample of measurements is given Y 8 4 2 2 0 8. Compute the coefficient of...
5 A sotware package consists of 9 programs, 4 of which must be upgraded. 3 programs are randomiy dhosen for testing Construct the distribution law for the number of programs that must be upgraded among chosen. 6. The distribution law of random variable X is given 01 04 03 02 Find the variance of random variable X 7. Let X be a continuous random variable whose probability density function is: 2x3+ax2, ifx E (0; 1) if x (0;1) f(x) 0,...
6. Let X be a continuous random variable whose probability density function is: 0, x <0, x20.5 Find the median un the mode. 7. Let X be a continuous random variable whose cumulative distribution function is: F(x) = 0.1x, ja 0S$s10, Find 1) the densitv function of random variable U-12-X. 0, ja x<0, I, ja x>10.
5. Find the moment generating function of the continuous random variable X whose a. probability density is given by )-3 or 36 0 elsewhere find the values of μ and σ2. b, Let X have an exponential distribution with a mean of θ = 15 . Compute a. 6. P(10 < X <20); b. P(X>20), c. P(X>30X > 10), the variance and the moment generating function of x. d.
4. Let X be a continuous random variable with probability density function: x<1 0, if if| if x>4 f(x) = (x2 + 1), 4 x 24 0 Find the standard deviation of random variable X.
5. (20%) Let X be a continuous random variable whose probability density function is fr(x) (a +bx)%0(x) (a) If Ex)f find a and b. (b) Give the cumulative distribution function F,(x) f()dt of X and Var(X) (c) Let A be any Borel set of R. Define P by P(A) [,f dm
5. (20%) Let X be a continuous random variable whose probability density function is fr(x) (a +bx)%0(x) (a) If Ex)f find a and b. (b) Give the cumulative distribution...
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...
13. Let X be a continuous random variable with density P(X0)0.3 and P(X 1) 0.7. Find (i) 1 - Fx(t) where Fx(t) is the cumulative distribution function of X (i) 1-Fx (t) da (iii) 0-P(X = 0) + 1 . P(X = 1) 0
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