If the probability density of a random variable is given by f( x ) = k ( 1- x² ) for 0 < x < 1 O else where. Find the value of K and the probabilities that a random variable will take on a value i) between 1 and •2 ii) greater than 5.

Q: If X has an exponential distribution with the param-eter θ, use the distribution function technique…

A: A continuous random variable X is said to be follow exponential distribution with parameter θ if the…

Q: Suppose that the random variable X has the probability density function ´c(1- x²) for - 1< x s1 f(x)…

A: Given that  Probability density functions of X is  f(x)= c(1-x2)   , -1&lt;=X&lt;=1       = 0…

Q: Suppose X is a random variable taking values in the interval [0,2] with probability density function…

A:

Q: If the probability density of a random variable is given by 0<x<1 f(x) ={2-x 1<x< 2 0 elsewhere…

A: Given,f(x)=x0&lt;x&lt;12-x1≤x&lt;20elsewhere

Q: Let X1,.X, be a random sample from a uniform (0,0) distribution and let Y = max(X1,..., the coverage…

A: We have a sample X1, X2,....,Xn from uniform distribution.  We know that, Y = max(X1, X2,....,Xn) =…

Q: The continuous random variable X has a pdf fy (x) = x/2, 0<x< 2. Twn independent determinations of X…

A:

Q: Suppose that the random variable X has the probability density function for -1 s x s 1 c(1- x2) f(x)…

A:

Q: 2.30 Let X be a single observation from a population with probability density function f(x): 80 e<x<…

A:

Q: Let X be a random variable representing a risk with E(X) = 10 and E(X²) = 125. A portfolio contains…

A:

Q: Find the probability that none of the three bulbs in a set of traffic lights will have to be…

A:

Q: 1. Suppose the random variable X has a pdf given by that this is a valid pdf. If 0 ≤x≤a, find a so

A: Let X be the random variable having probability density function (pdf) is,  f(x) = (1/2)*x2, if…

Q: Consider a random variable X with E[X] = 10, and X being positive. Estimate E[ln square root(X)]…

A: The Jensen's inequality is defined as: If p(x) is a convex function then E[p(x)]≥p[E(x)]. Also, a…

Q: Let X be a random variable representing a risk with E(X) = 10 and E(X) = 125. %3D A portfolio…

A: Given  E(X)=10, E(X2)=125, n=25  Note this Probability value calculated from standard normal…

Q: 2. Suppose that a continuous random variable X has PDF f(x) = }7 (1 – x²) -1<x<1 else

A:

Q: Find the probability that none of the three bulbs in a set of traffic lights will have to be…

A:

Q: The time it takes to repair a personal computer is a random variable whose density, in hours, is…

A: Let X be a continuous random variable with probability density function fx. The expected value of…

Q: The score of a student on a certain exam is going to be a number between 0 and 1. Think of it as the…

A: The probability density function is given as  f(x) = 4x0≤x≤124-4x12&lt;x≤10otherwise The cummulative…

Q: If the continuous random variable X has the probability density ( 62(1 - 2) for 0<z<1 elsewhere f(2)…

A:

Q: 5. Suppose that X is a continuous random variable whose probability density unction is given by…

A: Given density function, f(x)=C(4x-2x2), 0&lt;x&lt;2 The value of C is obtained by using the…

Q: 1. If the probability density of the random variable is given by 630x (1- x) for 0<x<1 flx) =…

A: Given: The distribution given is as follows fx=630 ×x4×1-x4             0&lt;x&lt;1

Q: The random variable X has probability density function 1 < x < 2 f(x) = otherwise. Calculate Var(4X…

A:

Q: Suppose that X is the length of time (in minutes) that a customer queues in a bank. The probability…

A:

Q: Given an n dimensional random sample X from a population with density f(x,0). Show at maximizing the…

A:

Q: An automobile manufacturer road tests a large sample of its subcompacts to determine gas…

A: Solution

Q: Let X be a continuous random variable with density f (x) = 24x-4 for æ > 2. Then Var (X) is equal to

A:

Q: 48. If two random variables x1 and x2 have the joint probability density f (x1, x2) = - (x + 2x2) }…

A:

Q: Since the probability function of the continuous random variable X that does not take negative…

A: From the given information, f(x)=1(1+x)2 Given that the continuous random variable X that does not…

Q: If X is a continuous random variable with probability density function: (2-x) 0<x<2 f(x) = {1"…

A: Step 1: Given the probability density function,                                   f(x)= 34x(2-x)…

Q: A random variable X has a Pareto distribution if andonly if its probability density is given by f(x)…

A: Note: The pdf is unclear in the question, hence solved for a two-parameter Pareto distribution: The…

Q: The probability density function of X, the lifetime of a certain type of electronic device (measured…

A: Solution

Q: Suppose that X|A = 1 ~ Poisson(A) and that ^~ Gamma(a, B) (A priori distribution). Prove using the…

A: We have,

Q: According to the Maxwell–Boltzmann law of theoret-ical physics, the probability density of V, the…

A:

Q: 2 If the probability density of a random variable is given by (k + 2)x³ 0 < x < 1 f(x) = 0.…

A: f(x)=(k+2)x3        0&lt;x&lt;10                           o/wproperities∫f(x)dx=1

Q: Suppose that the random variable X has the probability density function for -1 s x s 1 c(1– x²) f(x)…

A:

Q: The probability that the percentage of salts in sand from a particular source does not match is 0.1,…

A:

Q: If the random variable T is the time to failure of a commercial product and the values of its…

A:

Q: The discrete random variable X has probability mass function kx x = 2,3 2kx P(X = x) = x-1' x = 4,5…

A:

Q: If X is an exponential random variables with rate 1, then its distribution function is given by…

A: Here it is given that , F(x) = 1 − e−x Let us consider , F(x) = u. Now the distribution function…

Q: Find the cumulative distribution function of the random variable X whose probability density is…

A: As the graph given above in question: It is clear that fx≥0, for all x∈ℝ. So,…

Q: 6) Allow a continuous probability distribution to be defined as f(x) = 4x³ for the range 0 SXS1.…

A:

Q: Given an n dimensional random sample X from a population with density f(x, 0). Show that maximizing…

A: We know that the fuction x↦ln x is strictly increasing. Let θ' be the value maximizing Lθ/x and θ''…

Q: find the probabilities that a random variable having this probability density will take on a value…

A: Based on given probability density function, we have to find the probabilities P(0.2 &lt; X &lt;…

Q: A continuous random variable X has probability distribution function f(x) , where f(x) = k(1 − x2)…

A:

Q: Let X denote a random variable having a distribution. If F(x)=ax³ where 0≤x≤(+3). Find f(x) after…

A:

Q: Let the probability density function of a random variable X be ( 630 z (1- x)4 if 0 <I<1 f(z) =…

A: Probability density function of X; f(x)=630 x4 (1-x)4  if 0&lt; x&lt; 10…

Q: The probability that none of the three bulbs in a set of traffic lights will have to be replaced…

A:

Q: If the random variable X has the rectangular distribution over (0,1) show that the MGF of the random…

A:

Q: If the probability density of a random variable is given by |С ехр(-x/4), 0<x<1 fx (x) otherwise…

A:

Q: Probability and statistics

A: a.Computing the expected value of X:The expected value of X is given below: