show how to generate random variables from a uniform density on an interval (a,b)
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show how to generate random variables from a uniform density on an interval (a,b)
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- If X has a uniform density with α = 0 and β = 1, show that the random variable Y = −2. In X has a gamma dis-tribution. What are its parameters?There are 3 blue and 5 green marbles in a box. Balls are selcted at random, one after another without replacement, until a green ball is selected. Let X be a random variable whose value is the number of balls drawn. Find the density function of X.A continuous random variable X has a uniform distribution on the interval [−3,3]. Sketch the graph of its density function.
- An experiment consists of randomly drawing 3 cards from a standard deck (without replacement). The random variable Z is defined to be 2 times the number of face cards drawn which are not aces (jacks, queens, or kings). Find the density function of Z.Let x be a random variable with probability mass function given by: (image) Find V[X]Demonstrate the density function of the continuous uniform distribution from the data presented in the image.
- Show that if a random variable has a uniform density with parameters α and β, the probability that it will take on a value less than α+p(β-α) is equal to p.Suppose that X and Y are independent and uniformly distributed random variables. Range for X is (−1, 1) and for Y is (0, 1). Define a new random variable U = XY, then find the probability density function of this new random variable.the popularity density function f(x) for a uniform random variable X defined over the interval [2,10] is?
- Let X be a (continuous) uniform random variable on the interval [0,1] and Y be an exponential random variable with parameter lambda. Let X and Y be independent. What is the PDF of Z = X + Y.Let the radius of a circle be a random variable X with density function f(x) = 1 for 0 < x < 1 and f(x) = 0 otherwise. What is the probability density of the area of the circle?If a dealer’s profit, in units of $5000, on a new automobile can be looked upon as a random variable X having the density function Find the variance of X.