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- Consider the three functions I. f(x)= {1-x if 0 < x < 2 {0 otherwise II. f(x)= {1+x if 0 < x < 2 {0 otherwise III. f(x)= {(3/27)x^2) if 0< x < 3) {0 otherwise Which of these above functions can be probability distributions? And why?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 X
- 10) Let f(x) by the probability density function of some continuous random variable. Explain why it must be true that f(x) dx =1.2. Let X be a continuous random variable with probability density function (pdf) 3x�� 0Suppose Y - Uniform(01, 02) where the parameters 01 and 02 take the values 1 and 5 respectively. Compute the probability P(Y < y) when y=3.20.3. Consider the probability density function of a continuous random variable X f(x) = { − ³x + 1The random variable X has probability density function 3, 1< a < 2 f(x) = otherwise. Calculate Var(4X +7).Suppose 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.The random variable x follows a uniform probability distribution in the interval (0,1); the probability of obtaining x values outside this range is zero. What is the probability distribution of y = ln x?Let X be a random variable with pdf f(x) = kx*,-1The probability density function of the continuous random variable X defined in the set of non-negative real numbers is given as f(x) = 2.exp(-2x). What is the expected value of X?SEE MORE QUESTIONSRecommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSONA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON