Q3-1. A continuous random variable X that can assume values between x = 2 and x = 5 has a density function given by f(x) = 2(1 + x)/27. Find P(3.6sX <4). 0.142222222 0.241111111 0.175925926 0.362592593 0.418888889

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A: Consider the given joint density function:

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

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A:

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A: The median of a probability density function, f(x) is calculated using the formula,               ;…

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A: From the given information, FX=0, x&lt;-1x+24, -1≤x&lt;11, x≥1 From the above distribution function,…

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A: It is given that

Q: 8. A random variable has a probability density function given by (4 x - 1 f(x) = 0 ≤ x ≤ 1, ≤ 2, 1 ≤…

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

Q: The Gamma pdf for continuous random variable Y takes the form 1 ya-le-ylB y> 0 p«T(a)" f(V) = for a,…

A: Gamma pdf for continuous random variable Y; f(y)=1βαα!yα-1e-yβy&gt;0    0y≤0       for α,β&gt;0 if…

Q: 3. If a random variable has the probability density for x>0 2e-2* f(x) = for x <0 Find the…

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A: Given,  b0 = 0.16 b1 = 5.5 X = 20     To find the predicting value for y for X = 20.

Q: Since y; € {0, 1} (Bernoulli random variable), the joint density (pmf) of observing iid sample y =…

A: Given yi∈0,1 ( Bernoulli random variable and the joint density of iid sample y=y1, . . . , yn is…

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!