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7. Let X be a continuous random variable whose probability density function is: 2x3 +ax2, if...
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
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...
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
3. Let X be a continuous random variable with probability density function ax2 + bx f(0) = -{ { for 0 < x <1 otherwise 0 where a and b are constants. If E(X) = 0.75, find a, b, and Var(X). 4. Show that an exponential random variable is memoryless. That is, if X is exponential with parameter > 0, then P(X > s+t | X > s) = P(X > t) for s,t> 0 Hint: see example 5.1 in...
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. (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...
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.
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,...
Problem 8: Let X and Y be continuous random variables. The joint density of X and Y is given by: fxy (x, y)2 if 0 yx< 1. Find the correlation coefficient of X and Y, pxy.
Problem 8: Let X and Y be continuous random variables. The joint density of X and Y is given by: fxy (x, y)2 if 0 yx
7. Let X be a continuous random variable with probability density function: 0, 5+2x if if 0 if x> 10 x<b f(x)=re, 76-0 5310 x 10 150 o Find the expected value and mode of random variable X. Part 3. Statistics The following sample is given 3.15 3.25 3.25 3.35 3.45 3.5 3.5