Problem #9: Suppose that a random variable X has the following probability density function. (c(81-x²) 0≤x≤ 9 0 otherwise f(x) = Find the expected value of X. (You will need to find the value of the constant C so that f is a pdf.)
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- Problem 7: Let X be a continuous random variable with the probability density for f(x) = 3x2 values of x in [0,1], and f(x) = 0 elsewhere. Compute the expected value and variance of X.If X is a continuous variable in the range 3 > X > 0 and its distribution function is as follows: F ( x ) = k : ( x3 + x2) find the probability density function?Problem 1. A continuous random variable X is defined by f(x)=(3+x)^2/16 -3 ≤ x ≤ -1 =(6-2x^2)/16 -1 ≤ x ≤ 1 =(3-x^2)/16 -1 ≤ x ≤ 3 a)Verify that f(x) is density. b)Find the Mean
- Rework problem 16 in section 4.2 of your text, involving drawing markers from a box of markers with ink and markers without ink. Assume that the box contains 12 markers: 9 that contain ink and 3 that do not contain ink. A sample of 6 markers is selected and a random variable Y is defined as the number of markers selected which do not have ink. Find the probability density function. Be certain to list the values of Y in ascending order.Rework problem 16 in section 4.2 of your text, involving drawing markers from a box of markers with ink and markers without ink. Assume that the box contains 12 markers: 10 that contain ink and 2 that do not contain ink. A sample of 5 markers is selected and a random variable YY is defined as the number of markers selected which do not have ink. How many different values are possible for the random variable YY? Fill in the table below to complete the probability density function. Be certain to list the values of YY in ascending order.Question 17 If X is a random variable with the probability density function: f (x) = c|x|, for - 1 < x < 1 and 0 otherwise. What is the value of c? Please round your result to one decimal place. Correct Answer:_______________________
- Rework problem 16 in section 4.2 of your text, involving drawing markers from a box of markers with ink and markers without ink. Assume that the box contains 17markers: 15 that contain ink and 2 that do not contain ink. A sample of 3 markers is selected and a random variable Y is defined as the number of markers selected which do not have ink. How many different values are possible for the random variable Y? Fill in the table below to complete the probability density function. Be certain to list the values of Y in ascending orderRework problem 16 in section 4.2 of your text, involving drawing markers from a box of markers with ink and markers without ink. Assume that the box contains 13 markers: 11 that contain ink and 2 that do not contain ink. A sample of 4 markers is selected and a random variable YY is defined as the number of markers selected which do not have ink. How many different values are possible for the random variable YY? Part 2 Fill in the table below to complete the probability density function. Be certain to list the values of YY in ascending order.What is the value of the constant c for p(x) to qualify as a probability mass function? ?(?)=?(1/4)x-1 ?? ? = 1, 2, 3, 4, 5, ... and p(x) = 0 otherwise. How would you get c{1-1/4}-1 = 1
- Rework problem 16 in section 4.2 of your text, involving drawing markers from a box of markers with ink and markers without ink. Assume that the box contains 19 markers: 14 that contain ink and 5 that do not contain ink. A sample of 8 markers is selected and a random variable Y is defined as the number of markers selected which do not have ink. How many different values are possible for the random variable Y? Fill in the table below to complete the probability density function. Be certain to list the values of Y in ascending order.2.1 The demand for a product varies from month to month. Based on data from past years, the following probability density function shows the probabilities of MNM company’s monthly demand. Probabilities of MNM company's monthly demand Unit Demand P(X=x) 1200 0.19 2100 0.30 3300 0.40 3800 0.11 a) What is the probability that MNM will sell 3300 units next month? b) Given the information above, how many units can they expect to sell in a month?Rework problem 5 in section 4.2 of your text, involving the selection of two students from a committee of students. Assume that the committee is made up of 3 males and 4 females. Two are selected at random, and a random variable X is defined to be the number of females selected. Fill in the table below to complete the probability density function. Be certain to list the values of X in ascending order. Value of X Probability 0 1 2
