Let the cumulative distribution function of a distribution is given by: 0, 1/2, 0 3.5. Determine the probability density function f(x) of the distribution.
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- Let f(x) = x for 0 < x < 1. Is f(x) a legitimate probability distribution function (pdf) for a continuous random variable? No, the area under f(x) is not 1 (it is greater than 1). Yes, all criteria for a pdf are satisfied. No, the area under f(x) is not 1 (it it less than 1). No, f(x) is not non-negative.Determine the conditional probability distribution of Y given that X = 2. Where the joint probability density function is given by f(x,y)= 1 - (x + y) for 1 < x < 4 and 0 < y < 3.A scout on a camping trip is requested to find some dry sticks of length at most one metre to use as firewood. A model for the distribution of the lengths, X, in metres, of sticks that she brings back to the camp has probability density function f(x) = VT, 0< x < 1. 0 < x < 1. According to the model, what is the mean length of the sticks that the scout brings back?
- Attention span in a population of students in a 50 minute class are found to be uniformly distributed with the given probability density function: {6 f(x) = { 10 ≤ x ≤ 50 otherwise a) What must c be equal to for this to be a valid probability density function? b) Determine the mean and median attention span of the students. c) Determine the standard deviation of the attention span of the students.The probability density function for a continuous random variable X is given by 0 < x < 1 1≤ x ≤ 2 else Find P(0.5 < X < 1.5) Round to 4 decimal places if needed. f(x) = X 2-xLet X be a random variable with a uniform distribution on the interval (0,1). Given Y = e*, derive a) b) the probability distribution function of Y = ex. the probability density function of Y.
- 5. Let X be a random variable with a uniform distribution on the interval (0,1). Given Y = e, derive a) b) the probability distribution function of Y = e*. the probability density function of Y.The random-number generator on calculators randomly generates a number between 0 and 1. The random variable X, the number generated, follows a uniform probability distribution. (a) Identify the graph of the uniform density function. (b) What is the probability of generating a number between 0.37 and 0.69? (c) What is the probability of generating a number greater than 0.83? ... OA. В. OC. Density 1.2- A Density 1.2- ADensity 1.2- 1- 1. 1- 0.8- 0.8- 0.6- 0.4- 0.2- 0+ 0.8- 0.6- 0.6- 0.4- 0.2- 04 0 0.2 0.4 0.6 0.8 1 0.4- 0.2- X 0- 0.2 0.4 0.6 0.8 1 1.2 1.2 0.2 0.4 0.6 0.8 1 1.2 (b) The probability is (Simplify your answer.) (c) The probability is (Simplify your answer.) B.Let x be a continuous random variable that has a normal distribution with u = 50 and o = 8. Find the probability P(30 ≤ x ≤ 39).