Consider a random variable X with E[X] = 10, and X being positive. Estimate E[ln square root(X)] using Jensen’s inequality.

Q: A random variable X has probability density function (x² + 2x + 4) for 0 < x < 3 f(x) = otherwise.…

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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: Q8 Marginalize the joint probability PMF's. mass function of X and Y in the previous qusetion to get…

A: Introduction: Consider a jointly distributed pair of random variables, X and Y, with joint…

Q: -2x f(x) 0, otherwise Let X be a random variable whose probability density function is given by what…

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Q: Find the equation of the normal line to the graph of f(x) = 2" log2 x at the point where x = 1.

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Q: For c in R, calculate E[e^cX] where X is exponential distribution.

A: In question, We'll find the E(e^cx) that is mgf of X, where X from exponential distribution. The…

Q: Suppose lifetime of a particular type of old mobile, X, can be modelled by the probability density…

A: The probability density function of X is obtained below: f(x)=0.5e-0.5x;x≥0 where x is a random…

Q: F of X and be-byu(y)

A: It is given that X and Y are independent events andZ=X+Y. The value of fXx is , fXx=ae-axux. The…

Q: If X is an exponential random variable with parameter 1 = 1, compute the probability density…

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

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Q: Prove that E(x) %3D Write the cumulative distribution function F(x).

A: The E(X) can be calculated as ∫0∞x·fxdx And the cumulative function F(x) is defined as Fx=PX≤x

Q: if x 2 1, Let {x2 0, if x < 1. Show that f is a probability density function and that the…

A: Topic:- probability density function  Note:- as per our guideline if more than one question uploaded…

Q: Let X be a random variable whose probability density function is given by -2kx f(x) = +-e-kr x > 0…

A: Given that k=0.75 And the probability density function is, f(x)=e-2*0.75x+12e-0.75x, x&gt;0…

Q: A lamp has two bulbs, each of a type with an average lifetime of 10 hours. The probability density…

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Q: Calculate the probability of finding the particle within the finite wall of the box when the…

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Q: X follows a gamma distribution with PDF  f(x) = 4xe-2x , where X > 0 (a) Derive E(Xn ).

A: Given,  fx=4xe-2x, x&gt;0 Therefore, Exn=∫0∞xnfxdx=∫0∞xn×4xe-2xdx=∫0∞4×xn+1e-2xdx=4×∫0∞xn+2-1e-2x dx

Q: Let X be an exponential random variable with parameter = 7, and let Y be the random variable defined…

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Q: Let the probability density function of a random variable X be 630r (1 – 1)* if (0 <I<1 f(z) = .…

A: Given

Q: Find (a) the mean of the distribution, (b) the standard deviation of the distribution, and (c) the…

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Q: The random variable is said to follow the distribution of Benford’s Law if P(X=i)=log10(1+i)/i…

A: The given probability mass function is as follows:

Q: The density function of a random variable is given as fx(x) = ae-bx x20. Find the characteristic…

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Q: Let X be a random variable with the gamma probability density function. Derive the MSE of T=X2+2X

A: Gamma distribution: It is a continuous random variable, with the probability density function of…

Q: The life (in years) of a laptop battery has a probability density function defined by P(x) -z /5 5…

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Q: Let X be a random variable with probability density function given by x -1 0 1 f(x) a b 0.25 If E(x)…

A: Given, x -1 0 1 f(x) a b 0.25 E(x)=0

Q: The random variables U1 and U2 are independent, and each has an exponential distrib with rate…

A: From the given information, U1 and U2 are independent and each has an exponential distribution with…

Q: A2. Suppose that the continuous random variable x has the probability density function 1 f(x) -…

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Q: The life (in years) of a laptop battery has a probability density function defined by P(x)=12e−x/2…

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Q: Suppose that a random variable X has a continuous distribution with the probability density function…

A: Answer:-  Given X has a continuous distribution with the probability density function…

Q: 5.

A: The probability density function of the random variable Y defined by Y = log X is obtained below:Let…

Q: The life (in years) of a laptop battery has a probability density function defined by…

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Q: For a particular kind of battery, the probability density function for x hours to be the life of a…

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Q: The pdf (probability density function) of a random variable X, px(x), has the following property:…

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Q: Verify that p(x) = 3x−4 is a probability density function on [1,∞) and calculate its mean value.

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Q: Find the mean value of random variable X, if X has the following density function, f(x) = 1-x²,…

A: The mean value of X can be obtained as E(X) = ∫x.f(x) dx

Q: If the probability density of X is given by f(x) =kx3(1 + 2x)6 for x &gt; 00 elsewhere where k is an…

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Q: A study shows the daily number of hours X that a teenager watches television and the daily number of…

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Q: Let X be a random variable with probability density function a+ bx², 0<x<1 f(x) = | 0, otherwise If…

A: We have given that, Let X be a random variable with probability density function…

Q: The probability density function of a random variable is kVx+ – 1 f(x) - if 1 s x< 2

A: Hello! As you have posted 3 different questions, we are answering the first question. In case you…

Q: A continuous random variable X has the following density function, * find the expected value of…

A: This can be solved using expectation formula

Q: Let X be an exponential random variable with the following probability density functioi x20 f(x;2)={…

A: Solution: Let X be an exponential random variable having probability density function…

Q: What is the joint probability density function f₁,2 of Y₁ = X₁/X₂ and Y₂ = X₂?

A: We will use Jacobian method of transformation to find the joint probability of Y1 and Y2.

Q: et X be the number of litres of milk shake that is requested at a café on a hot summer day. Assume…

A: According to question, we have to find c such that, P(X&lt;c) = 0.95. Using Ti-84 calculator, we…

Q: Let X be a random variable with density function (2x² -1<x< 3 3 f(x) = - 0, elsewhere Find the…

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Q: Suppose that X is a continuous random variable with a probability density function is given by f(x)=…

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Q: The random variables X and Y have a joint probability density function given by f(x,y) = wxy, 0 < x…

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Q: suppose x has an exponential distribution with probability density function f(x) =2e^-2x, x>0. Then…

A: In question, Given X has an exponential distribution with probability density function f(x) =2e^-2x,…

Q: Let X be a random variable with probability density function L{(1 }(1– æ), -1 < x < 0 f(x) = 0,…

A: Given : f(x) = 23(1-x) , -1≤x&lt;0

Q: Let X be a continuous random variable with probability density function 2x f(x; 0) for x > 0 (and…

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Q: Let X be a random variable with the probability density function, Oe-ex 0 < X < ∞; f (x) = { 0,…

A: Given: The probability density function of a random variable X is given as:…

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.