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part c and d im stuck on
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- The random variable X models the loss in thousands of dollars due to a fire in a commercial building. Its density function is f(x) = 0.005*(20-x) for 0 being less than or equal to x and x being less than or equal to 20 and f(x)= 0 otherwise. Given that a loss due to the fire exceeds $8000, find the probability the loss exceeds $16000.Probability density function of the random variable X (pdf) fX(x) = ( c(1 − x2) −a ≤ x ≤ a ( 0 d.y get given in the form. Event |X − b| < a/2 defined as. variables a, b to probability rules randomly give the appropriate values. After determining the values of a, b; Under the condition A of the random variable X Find the probability density function.The random variable X has a uniform density function over the interval [-1, 1]. a. Sketch the probability density function of X. Find the mean and variance of X .
- The probability density function of the X random variablelike this.a. The probability of a random variable U defined as U = X^2Find the density function.b. V = 1/X Find the probability density function of the random variable V defined as.continuous random variable has probability density function given by F(x) =k(2x+3) 1<=x<=2 0 ,otherwise Find k if f(x) is a probability density functionFind Value of k P(1.5<=x<=4) ?Numbers X and Y between 0 and 1 are chosen randomly. The joint probability density is p(x, y) = 1 if 0 < x < 1 and 0 < y < 1, and p(x, y) = 0 otherwise. Calculate the probability P that the product XY is at least ½.
- Proof Let X be a random variable with EX2 < ∞ and let Y = |X|. Suppose that X has a Lebesgue density symmetric about 0. Show that X and Y are uncorrelated, but they are not independent.The time X of a certain chemical reaction, measured in hours, has the probability density function f(x) = -2x + 2 over the interval [0,1]. A. Draw the draw of this probability density function. B. Verify that it is a probability density function of a continous random variable X. C. Find the probability that the time of a reaction more than 0.5 hour.The pdf (probability density function) for the CONTINUOUS random variable X is given as: f(x) = { (1/5)e^(-x/5); x>0 ] 0; elsewhere a. Show that f(x) satisfies the properties for a pdf. b. Find the CDF of X. c. Find P (x ≥ 5) using pdf and CDF.
- Two discrete random variables X and Y have the joint probability density function: f(x.y)=e*p" (1-p)* y!(x-y)! x-y ,y 0,1,2,..,x; x 0,1,2,... where 2, p are constants with 2 >0 and 0 <p<1. 1. Find the marginal probability density functions of X and Y. 2. Find the conditional distribution of Y for a given X and of X for a given Y.Buses depart from a bus stop every 10 minutes from 00:00. One person came to the bus stop without knowing the timetable. Let's say he will take the bus. The random variable X denotes the time this person has to wait. Find R_X and f_X. (R_X denotes the image of X and f_X denotes the probability mass/density function of X)A random variable X has the density function: f(x)= K.1/(1+x2), ?? − ∞ < x < ∞ . Determine K and the c.d.f. associated with. Evaluate the probability P(X≥ 0). Find also the mean and variance of X.