ing the i

Q: (37) Let X be a random variable with p.d.f. (x+1)e2* x=1,2,3 f(x) =- , find (1) k (2) E(x² +1) O.w

A: The probability distribution table is obtained as :  x 1 2 3 f(x) 2e2k 3e2k 42k Every…

Q: Each front tire on a particular type of vehicle is supposed to be filled to a pressure of 26 psi.…

A: To compute the covariance between X and Y, we need to find the expected values (means) of X and Y…

Q: 1. Assume that X is a discrete random variable with E(X) = -2, E(X²)= 9, E(X) = -5. and %3D %3D…

A: E(X)=-2E(X2)=9E(X3)=-5

Q: Each front tire on a particular type of vehicle is supposed to be filled to a pressure of 26 psi.…

A:

Q: Let F(x) be the cumulative distribution function (cdf) of a random variable X. Which of the…

A: P(a<X<b) = F(b) - F(a) F(a) + P(a<X<b) = F(b)

Q: Let X1,...,Xn be a random sample from a distribution with mean μ and variance σ2. Find the value of…

A: Given X1, X2, ……, Xn be a random sample from a distribution with mean µ and variance σ2.

Q: 2. Let X and Y be two arbitrary random variables. Define the conditional variance of X given Y by…

A: Let X and Y be two arbitrary random variables. Define the conditional variance of X given Y…

Q: a) Compute E(X) and V (X). b) Compute the expected number of pounds left after the next customer's…

A: The variable X denotes the number of lots ordered by a randomly chosen customer.

Q: Let X1,..., XN be i.i.d. random variables with a uniform distribution of (0, 0]. Consider the…

A: Solution :

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: Let X be a discrete random variable such that P(X = n) = (1 − p)"−¹p. Prove that E(X-¹) = -pln(p)…

A:

Q: 3. Let X be a random variable that is equal to the number of times a six-sided die lands on 6 over…

A: Possible outcomes for :- X=0 : No sixes in two rolls.- X=1 : One six in two rolls.- X=2 : Two sixes…

Q: Given a random variable X with anf(x) = x between 0 and 1, with an f(x) = x/3 between 1 and 2, and…

A: The probability density function (PDF) of the random variable  is given by,

Q: Let pX(x) be the pmf of a random variable X. Find the cdf F(x) of X and sketch its graph along with…

A:

Q: A random variable X has pdf fx (x) = e¬* for x 20. Use Chebyshev's inequality to show that P 1X – 11…

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Q: 4. Let X₁, X₂ be i.i.d. Exponential (A) random variables. Define Z = I(X₁ + X₂₁ > 7) = { Find…

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Q: Let X and Y be independent uniform random variables on (0,1). Let Z = [1/(X + Y)]. (Recall that is…

A: Let X and Y be independent uniform random variables on (0,1). And let Z = [1/(X + Y)].Then (a) Find…

Q: Suppose X and Y are two independent and identically distributed geometric random rariables. The pmd…

A: PMF of X is given by, P(X=x) = p(1-p)x-1 , x=1,2,3.... Now,  ⇒P(X≥x)= ∑t=x∞ P(X=t)= ∑t=x∞p(1-p)t-1 =…

Q: (a) Let X be a random variable with finite variance. Let Y = ax + 3 for some numbers a, ß E R.…

A: In this problem, we are examining the computation and interpretation of two quantities, , related to…

Q: Let X1, X2, ..., Xn be a random sample from a population r.v. X, with range Rx C [a, b].…

A: Given information: It is given that X1, X2, … , Xn be a random sample from a population of random…

Q: Let X be a random variable having a cumulative distribution function F. Show that if EX exists, then…

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Q: . At a particular gas station, gasoline is stocked in a bulk tank each week. Let random variable X…

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Q: The CDF of a random variable X is X 1/2]? b. What is P[-1/2 < X < 3/4]? c. What is P[|X|< 1/2]? d.…

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Q: Let X(t) be a WSS random process. Show that for any a > 0, we have P{|X(t +T)= X(t)| > a} < 2Rx(0) -…

A: From the given information, X(t) be a WSS random process with parameters EXt=0 and RXτ. Consider,…

Q: Let X and Y be independent random variables, both being equally likely to be any of the values 1, 2,…

A: The  and  are independent random variables. and takes equally likely to be any of the values .

Q: Show that the characteristic function of a random variable X satisfies |1 - 0(t)| ≤ EtX.

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Q: Jordan is practicing field goals. On each attempt, he have a 0.35 chance of making it. Let X be the…

A: It is given that n=5 and p=0.35. (i) EX=n×p=5×0.35=1.75

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: If x is a random variable such that x-b(1,2) then P(V ( x) <x<E (x ) )is? X

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Q: Suppose the random variable X has pdf K exp 12V/28 XP ( - ("=2)²). fo 2√/2K 0. £x(u) = 0≤u≤ 4,…

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Q: 11. Let f(z) and F() denote, respectively, the PDF and the CDF (cumulative distribution function) of…

A: Given: X is a random variable with PDF as fx and CDF as Fx. The conditional PDF of X given X&gt;x0…

Q: Let X be an exponential random variable with standard deviation σ. Find P(|X − E(X)| > kσ ) for k =…

A: Let X be the random variable distributed exponentially with parameter λ.   Since the standard…

Q: 7 The function f(t) - 7t/3 e models a continuous probability for 0 <t < o. 3 Compute the median:

A:

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

A: (a) We know, ∫fx dx=1∫02k+4x+2 dx=1∫02kx+2k+4x+8 dx=1kx22+2kx+2x2+8x02=12k+4k+8+16=16k=-23k=-236

Q: 2. Let X be a discrete random variable whose range is the nonnegative integers. Show that E[X]=…

A: # discrete random variable x with non negative integers  Then to prove that E(x)=sum(1-F(x))  F(x)…

Q: { x < -5 (x + 5)2/144 –5 < x < 7 Fx(x) = 1 a ) ΕX] b) ož X c) E[X*]

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Q: Define the discrete random variable, Xn (w), as follows: Xn = Ei=1<x<} * Show that for every w N,…

A: To show that for every ω ∈ Ω, Xₙ(ω) ↑ X(ω) as n → ∞, we need to prove that Xₙ(ω) is a monotonically…

Q: Suppose the random variable X has pdf K 2√/27 (xp ( - (a − 2)²) - £x(u) = 0 ≤u≤ 4, otherwise. where…

A:

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!