wise. What is the joint probability density function of Y₁ = X₁/X₂ and Y₂ = X₂?
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- Q. 6 Find 30th percentile, median and 70th percentile for the following probability density functions: X < 0 0s X < 1 0s X s 1.3 1.3 (i) fx(x) = 3x2 1s Xs 2 (ii) fx(x) = %3D %3D 2-x 1.3 < X s 2 14 otherwise 0.7 otherwise1. or a cumulative distribution funetion (cdf). Decide if the function graphed below is a probability density function (pdf) 2c 4 8.The table below shows an incomplete probability density function for X , the number of imperfections per batch of jeans that just came off a production line. What should the missing probability be? Provide the final answer as a decimal. x P(X = x) 0 0.88 1 0 2
- e Define and explain joint distribution function and joint density function of two random variables X and Y.Q.2 Let X has the following probability density function: fx(x) = a e-ax;x > 0 Find moment generating function and then using it find mean and variance. End of QuizConsider the following probability density function, what is the F(14) 0.22 x = 7 x = 9 x = 11 x = 13 x = 15 x = 17 0.22 0.05 0.05 f(x) = %3D 0.06 0.33 0.06 0.01 x= 19 x = 23
- 2. Consider a gas station's daily sales. Let Y be the volume of gas sold per day in 1000s of gallons. Assume the distribution of Y follows this pdf: 1sxs 2 S (v) . else What value of k is required for the above function to be a valid pdf? b. Verify that the function given is a valid probability density а. function c. Determine the cumulative distribution function (cdf) of the random variable d. Compute the probability that there is exactly 1500 gallons of sales on a given day (Hint: Find?(r - 1.5)) = 1 CO0Write CLearly plzFind the mean and variance of X given the following probability density function:
- Question 2. A continuous random variable, X has the following probability density function: S(x) = cx² 0sxs10 = 0 otherwise a) Find the value of c. b) Find the mean, median, mode, standard deviation and coefficient of variation. c) Find the probability that X is greater than 3.0 given that X is between 2.0 and 5.0.Please give answers of my questions that I have uploaded as an image.