9. If X is a continuous random variable with probability density function given by f(x)=k(x-x³) <=0 0≤x≤1 otherwise
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- 7. If a random variable has the probability density function -1≤x≤3 otherwise f(x)=k(x²-1) =0If the probability density of X is given by f(x) =2x−3 for x > 10 elsewherecheck whether its mean and its variance exist.5. Suppose that X is a continuous random variable whose probability density function is given by C(4x-2x2) 0 < x < 2 f(x) = otherwise What is the value of C?
- Suppose that therandom variable X has the probability density function c(1– x2) for -1s x <1 f(x) elsewhere What is the variance of X4. Let X be a random variable whose probability density function is given by 3 0≤x≤2 3 2≤x≤2 elsewhere k. f(x) = {k .(2-x), 0, Determine cumulative distribution function of X. (10)If the probability density of a random variable is given by fx(x) = K(1-x²) 0Suppose that the continuous random variable X has cumulative distribution function given by F(x)= 0, if x < sqrt(2); x2-2, if sqrt(2) <= x <= sqrt(3); 1, if sqrt(3) <= x Find the probability density function of X.4. A continuous random Variable X has probability Density function defined by f(x) = 5-5x; 0<=x<=1, =0 otherwise, find the mean and the variance of the distribution.Suppose that the random variable X has the probability density function for -1s x <1 c(1- x2) f(x) elsewhere What is the variance of X A 1/3 B 1/5 (c) 1/2 D 1/4The shelf life (in hours) of a certain perishable pack-aged food is a random variable whose probability density function is given byf(x) =⎧⎪⎪⎨⎪⎪⎩20,000(x + 100)3 for x > 00 elsewhere Find the probabilities that one of these packages will havea shelf life of(a) at least 200 hours;(b) at most 100 hours;(c) anywhere from 80 to 120 hours.Let X be a continuous random variable with PDF 3 x > 1 x4 fx(x) = otherwise Find the mean and variance of x.2. If the random variable X has the probability density function f(x) = (1-x²), -1 < x < 1, 3 4 what is the variance of 15X + 2?SEE MORE QUESTIONS