Let R have probability mass function (pmf) p(r)=1/8 for r=1,2,...,8. Fin (1)the cumulative distribution function (cdf) of R; (2)P(R>5); (3)E(R):
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![Let R have probability mass function (pmf) p(r)=1/8 for r=1,2,...,8. Find
(1)the cumulative distribution function (cdf) of R;
(2)P(R>5);
(3)E(R);
(4)E(R²):
(5)E[(R-3)(R-1)];
(6) Var(R).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7612013f-aa44-4e87-9119-d1d4f6335a4f%2F628057ad-3e00-4757-b0f7-882788017bb1%2Fah8433t_processed.png&w=3840&q=75)
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- X is an exponential random variable with λ =1 and Y is a uniform random variable defined on (0, 2). If X and Y are independent, find the PDF of Z = X-Y2X is a discrete random variable that takes values (1, 2, 3, 4, 5). P(X=3)=0.6 and P(X=5)=0.25. What is the cumulative mass function for X=5, i.e. F(5)?If two random variables X1 and X2 have the joint density function given by f (x1, x2) = x1x2, 0 < x1 < 1, 0 < x2 < 2 0, otherwise Find the probability that (a) Both random variables will take on values less than 1 (b) The sum of the values taken on by the two random variables will be less than 1.
- A continuous random Variable X has probability Density function defined by f(x) = 5-5x; 0Consider two random variables X and Y whose joint probability density function is given byf_X,Y (x, y) = c if x + y ≤ 1, x ≤ 1, and y ≤ 1,0 otherwise What is the value of c?Find the probability mass function (pmf) and cumulative distribution function (cdf) of Y with Binomial Discrete Distribution with n=2 and p=1/2 or Y~Bi(2,1/2).
- Suppose X is a random variable taking values in the interval [0,2] with probability density function f(x) = 1-x/2. What is the variance of X?Find the moment-generating function of the continuous random variable X whose probability density is given by f(x) = 1 for 0 < x < 1 0 elsewhere and use it to find μ’1,μ’2, and σ^2.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.
- On a production line, parts are produced with a certain average size, but the exact size of each part varies due to the imprecision of the production process. Suppose that the difference between the size of the pieces produced (in millimeters) and the average size, which we will call production error, can be modeled as a continuous random variable X with a probability density function given by f(x) = 2, 5e^(-5|x|), for x E R (is in the image). Parts where the production error is less than -0.46 mm or greater than 0.46 mm should be discarded. Calculate (approximating to 4 decimal places): a) What is the proportion of parts that the company discards in its production process? b) What is the proportion of parts produced where the production error is positive? c) Knowing that for a given part the production error is positive, what is the probability of this part being discarded?Suppose the random variables X and Y have joint probability density function f(x,y) given by: (image)Find: P(X < Y) = fX|Y=y (x)Let x be a continuous random variable with the density function: f(x) = 3e-3x when x>0 and 0 else Find the variance of the random variable x.
