(52) Let X be a random variable with p.d.f. 1 5 0

Q: (17) Let X be a random variable with p.d.f. o >x>0 f(x)=< find E(e) O.w

A: Solution : Given :  f(x) = 15e-15x          0&lt;x&lt;∞0           o.w Here X ~exp(15) M.G.F of x is…

Q: 1. Let X be a random variable with a probability distribution Pr(X=1)=0=1-Pr(X=-1), where 1/2 <0 <…

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

Q: If the moment generating function of a random variable X is: (1/3+(2/3)e t ) 5 find P (X > 3).

A: The given moment generating function of a random variable X is 13+23et5.

Q: 2. A random variable X has pdf |x| < 1 elsewhere. cx(1+ x) a. Find c. b. Find E{X}and V AR{X} c.…

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Q: (1) Let X be a random variable with p.d.f. ke 2x f(x) ={ 0 <x<0 , then o.w (a) k=3 (b) k=2 (c) k =-…

A: Reviewing information, X is a r.v. with pdf, f(x)=k·e-2x                                   ;…

Q: (d) Determine the (marginal) distribution of air pressure in the right tire alone. for 20 ≤ ≤ 30 (e)…

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Q: Let X be a random variable with p.d.f f(x) = 2x,0 < x < 1. Find E(Vx) 2/3 5/4 3/2 O 4/5

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Q: Find E (X) and E(X²) and using these values evaluate E[(2X + 1)²]

A:

Q: Let X be a continuous random variable with the p.d.f f(r) = a2/24, if -2 < a < 4, and zero…

A:

Q: Suppose the random variable y is a function of several independent random variables, say…

A: Given that the random variable y is a function of several independent random variables, say…

Q: 6x) 0<x<1 S(x)%=D , then p(x<1) is (a) 1 (b) 2 (c) 3 (d) 4 (c) None of these

A: It is an important part of statistics. It is widely used.

Q: Let X be a discrete random variable with the following PMF: for x = 0 Px(x) = = 12 L3 L6 for x = 1…

A: Step 1:The probability mass function is given asx012P(x)1/21/31/6The range of the given PMF would be…

Q: 20) Let X be a random variable with p.d.f. k T<x<10 f(x) =- , find k. O.w

A: Solution: Let X be the random variable with pdf f(x) is  f(x)=kx       1&lt;x&lt;100      otherwise

Q: 13. The loss random variable X has a probability generating function 1 P(z) = = 2-z What is E[XA 3]?

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Q: Let X be a random variable distributed exponentially with parameter such that is 1/2 find the…

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Q: 1. The sum of two exponential random variables: 1.1 The standard exponential random variable has R…

A: Let x be a continuous random variable that follows  a standard exponential distribution with the…

Q: Let X be a positive random variable; i.e P(X ≤ 0) = 0. Which one is correct? (1) E (+) (²) (11)…

A: Given:X is a positive random variable, meaning .We need to determine which of the statements is…

Q: Suppose X has probability generating function GX(t) = 0.2 + 0.3t + 0.1t2 + 0.4t3. What is P(X = 2)?…

A: PGF of a Random Variable is given by, Gx(t) = Σ tx P(X=x)

Q: 16 a) A random variable has pdf £x (x) = ² (1-x²) fx 4 0 (1-x²) 0≤x≤1 Find E (4x+2) and E(x²). else…

A: Given information: f(x)=541-x4      ; 0≤x≤10                     ; Elsewhere

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: 0.1. Find P(E U F). 0.1 and P(F) The two events E and F are independent with P(E) = X

A: to work out the required probabilty

Q: A discrete random variable, X, has the following pdf as follows. X 0 1 2 3 4 P(X = x) 0.15 0.3 a 0.2…

A: Step 1: Given table, pdf tablex01234P(X = x)0.150.3a0.20.1 Step 2: a) The value of 'a' can be…

Q: Hom variable X has the gamma p. d. f with integer j rary ß>0, then E(Xk) is

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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: 3.2.13 Y is a continuous random variable with { 2(1- y), 0< y < 1; fy(4) = { 0, otherwise. Derive…

A: Let Y denotes the Continuous Random variable. From the information, given that

Q: 14. Let X be a discrete random variable with the following PMF 1 for k = -2 4 1 for k = -1 Px (k) 1…

A: Farmula used  Range=Maximum-Minimum

Q: Let A be the mean of the random sample drawn from a population whose pdf is given by fox =…

A: Note: Hi, thank you for the question. As per our company guideline we are supposed to answer only…

Q: E. Alex is back on Tinder. Let X, be a random variable that is equal to 1 if i-th person is a match…

A: Here, Xi's are Bernoulli trials which takes values either 0 or 1, with p = 0.50. Mean and standard…

Q: b) The continues random variable has the following probability density function; 0<x <4 12 f(x) 2<x…

A:

Q: Let Y be a discrete random variable with generating function 4 Gy (s) = 6 – What is Var(Y) (in…

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!