1 The continuous random variable X has p.d.f. f(x) where f(x) = ¿x for 0

Q: (a) f(x)= 5. For each of the following, determine the constant k so that f (x) satisfies the…

A: We have given that the random variable X having pdf in discrete form. Here, need to find out the…

Q: 4 The continuous random variable X has p.d.f. f(x) where for -3 2.5)

A:

Q: 82. Let X - Expo(A) and let Y be a nonnegative random variable, discrete or continuous, whose MGF M…

A: Given problem is :

Q: (45) Let X be a random variable with p.d.f. ((k + 4)(x+2) 0<x<2 f(x)=- find (1) k (2) E(x) O.W

A: (45) (1) The random variable X with p.d.f is, fx=k+4x+2      0&lt;x&lt;20…

Q: Let X denote the number of successes in a series of n independent Bernoulli trials with constant…

A: Given : Let X denote the number of successes in a series of n independentBernoulli trials with…

Q: A median of a distribution of one random variable X of the discrete or continuous type is a value of…

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Suppose f(x,y) = ry for 0<x<2, 0<y<2 then the mariginal probability distribution of X is 4

A: The marginal probability distribution formula of X is:

Q: Let X be a random variable with p.d.f. [(k +4)x 1<x<5 f(x) = , find (1) k (2) Var(x) O.W

A: Let X be a random variable with p.d.f. fx=k+4x      1&lt;x&lt;50                  otherwise   1) We…

Q: 62. Let X₁, i = 1, 2, ... be independent random variables all distributed according to the pdf fx…

A: The pdf is given as,A random variable is also defined here.The objective is to compute the variance…

Q: 1. Consider the cumulative distribution function for a continuous random variable X, if r 1 What is…

A: Given: The cumulative distribution function is as follows F(x) = x3     0&lt; x &lt; 1

Q: 21. Suppose that X and Y are jointly continuous random variable for 0 <x <1 and 1< y < 2 otherwise -…

A: From the given information, Consider, X and Y are jointly continuous random variable with pdf: fx,y…

Q: Let xy X2 Xn be a random sample from a distribution ...... with p.d.f. f (x, 0)= e- (x – 0); 0< x< ∞…

A: ANSWER: Form the given data,

Q: 3. Let X be a random variable with distribution function P(X ≤x} = { 0 x 1 if x ≤ 0, if 0 1. Let F…

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Q: Suppose that the random variable X has the following df. F(x) = {0 for x≤0, 1-ex for x>0 Determine…

A: The given dF is : F(x)=0for x≤01-exfor x&gt;0 We want to find quantile function.

Q: 7. Suppose random variables X and Y are independent. Let g(z) and h(y) be any bounded measurable…

A: The Given Random variables X and Y are independent. To show that CovgX,hY=0.

Q: 4. Let X be a random variable with c.d.f., 0, if x < 0 1 Fx (x) = • if 0sx < 1/2 2' 1, if x 2 1/2…

A:

Q: For the following discrete variable with probability f(x) X 1 2 3 4 f(x) 0.2 0.15 2с 0.05 0.15…

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Q: 3- Suppose that X and Y are independent and X,Y~ N(0,0²). Show that U and V are independent with…

A: Suppose W, Z ~i.i.dN0,1.  The joint probability distribution of W and Z can be written as follows:…

Q: Suppose that the waiting time X (in seconds) for the pedestrian signal at a particular street…

A: The random variable   represents the waiting time for the pedestrian signal. The PDF of random…

Q: (45) Let X be a random variable with p.d.f. ((k +4)(x+2) 0 <x<2 f(x)=- find (1) k (2) E(x) O.W

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Q: . Suppose the probability of selecting a number from the interval [0, 2] is given by f(x) = Cx. (a)…

A: Given f(x)=Cx, 0&lt;x&lt;2,

Q: (2) Let X be a random variable with p.d.f (3x² +6x) [>x>0 S(x) =- , then p(x < 1) is O.W (a) 1 (b) 2…

A:

Q: A relatively rare disease D occurs with P(D) = 0.001. There exists a diagnostic test such that: ●…

A:

Q: 11. The probability distribution function, P(X-x) of a discrete random variable X is defined as for…

A: Part a: We have been given the probability distribution function as, P(X=x)=27       for x=047…

Q: (24) Let X be a random variable with p.d.f. 2e-2x 0<x<0 f(x) =- , find E(e³*) O.w

A: Here,Ee5x=∫0∞e5xfxdx=∫0∞e5x2e-2xdx=2∫0∞e3xdx=2e3x30∞=23e3x0∞=23e3∞-e30=23∞-1=∞

Q: (7) Let X be a random variable with p.d.f. 1<x<0 f(x) = { ,find k. O.W

A: Reviewing information, X is a r.v. with pdf,f(x)=kx-2                          1&lt;x&lt;∞0…

Q: 3. Suppose X is a continuous-type random variable with p.d.f. f(t). How would you compute each of…

A: Given that the pdf of a continuous random variable X is ft. That is X~ft for t∈D, where D is the…

Q: = 4 and V(X) = 1, which of the following statements Let X be a continuous random variable that only…

A: Given mean=mu=4, variance=sigma^2=1 We solve by using chebyshev's inequality…

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!