To illustrate the proof of Theorem 1, consider the ran-dom variable X, which takes on the values −2, −1, 0, 1, 2, and 3 with probabilities f(−2), f(−1), f(0), f(1), f(2),and f(3). If g(X) = X2, find(a) g1, g2, g3, and g4, the four possible values of g(x);(b) the probabilities P[g(X) = gi] for i = 1, 2, 3, 4;(c) E[g(X)] = 4i=1gi ·P[g(X) = gi], and show that it equals xg(x)·f(x)

Q: (a) Two sets of n independent trials are performed, independently of each other, and each trial…

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Q: .6 (a) Two sets of n independent trials are performed, independently of each other, and each trial…

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Q: one of these

A: Sufficient

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Q: If X is a random variable, prove that Cov(X,X) = σX².

A: Let X is a random variable.

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Q: 0, elsewhere. Find the expected value and the covariance of g(X) = 4X + 3. %3D

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Q: If the p. d. f of a random variable X is f(x) = 1,0 ≤ x ≤ 2, then P(X> 1.5|X > 1) is

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Q: If X is a continuous random variable, argue that P(x1 < X < x2) = P(x1 < X < x2) = P(x1 < X < x2) =…

A: in the continuous random variables “≤” and “&lt;”, and similarly“≥” and “&gt;”, are interchangeable.…

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Q: 1. Show that B, and B are unbiased estimators of the true parameter ß. 2. Show that B1 is a linear…

A: Note: As per company guidelines only one question can be answered at a time. Kindly,  resubmit  the…

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A: Solution is given below

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Q: The diameter of a round rock in a bucket, can be messured in mm and considered a random variable X…

A: Given,f(x)=k(x-x4)     ; 0≤X≤10                 ; other wise

Q: Theorem 17-2. Let {T„} be a sequence of estimators such that for all ee 0, and (ii) Vare (T„) →0, as…

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Q: Suppose that f(x) = 1.5x² for −1 < x < 1. Determine the following probabilities: a) P(0 < X) = 0.5…

A: As per our guidelines we can solve first three sub part of question and rest can be reposted.…

Q: If X and Y are independent, then the conditional expectation of Y. given X is equivalent to: E(Y|X)

A: Here use basic definition of conditional probability and conditinal expectation

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Q: Theorem 3-14. For a fixed B with P( B) > 0, P (A \ B) is probability function.

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Q: * 2 نقطة واحدة 20 2. Under H., the likelihood function is given by L(4, af) = A. True B. False

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Q: Let X1, X2,...,X3 denote a random sample from a population having mean u and variance o2. 302 Which…

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Q: 8. Given two estimators X1 and X2 for a population mean, E[X1] = 6, V[X1] = 4, and V[X2] = 5. If the…

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Q: 1. What is the expectation of the function g(x1, x2) = x, using the following joint PMF? %3D X1 3 6…

A: The given function is gx1,x2=x1.

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Q: Consider the following function for a value of k. f(x) ={3kx/7,  0 ≤ x ≤ 1 3k(5 − x)/7 ,   1 ≤ x ≤…

A: As per our guidelines we are suppose to answer three sub parts.

Q: This result leads immediately to an important generalization. Consider a function of X and Y in the…

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Q: 1. Determine the requested probabilities. -2 -1 1. f(x) 0.2 0.1 0.4 0.2 0.1 a) P(xs 2) b) P(x > -2)…

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Q: Let X1 and X2be independent exponential random variables: fX1(x1) = e−x1 and fX2(x2) = e−x2 1

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Q: For RBD topology 1, the independent component working probabilities are: P(A)0.83, P(B)-0.73,…

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Q: The probability of the joint event {x₁ < X ≤ x₂, Y₁ <Y ≤ y₂} is given as P{x₁ < X < x₂, Y₁ <Y ≤y₂} =…

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A: Solution: Given information: n1= 200n2= 200x1= 126x2= 164p^1= x1n1= 126200= 0.63p2^= x2n2=…

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A: Given,the random varibles X1 , X2 are independent .

Q: as follows: 0 x 3) c) P(2<X<5) d) P(2 <X<5) 1.

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Transformation of Graphs

The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.

Exponential Functions

The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.