13. Let X be the number of heads in two tosses of a coin. (a) Find the probability distribution function of X. .T (b) Find the expected value of X. E(x) = Ex P(x) 0,1,2

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A:

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A: Given the probability distribution function of the maximum annual wind speed v is FVv=exp-vVc-γ with…

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Q: Let the function in the figure be a cumulative distribution function for the random variable X. Find…

A: For a finite random variable X, the cumulative distribution function is defined as F(x) = P(X ≤ x).…

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A: we have given - rt be a log return. Suppose that r0, r1 . . . are i.i.d. N(0, 0.0001). a) since ,…

Q: 6) (13 points) The random variable X has the following probability density function: x 1x(x)=2 0,…

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Q: Suppose the probability that Jimmy gets a hit on a given at-bat is 1⁄4. Let X denote the number of…

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Q: A weather forecaster predicts that the May rainfall in a local area will be between 1 and 7 inches…

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Q: Let X ∼ N(2, 4). (a) What is the distribution of (X−2) /2 ?

A:

Q: Let X be a random variable with the following probability distribution. Value X of X P(X=x) 0 10 20…

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Q: 16. For the probability density function shown, what is the probability of the random variable æ…

A: To find: The probability of the random variable x being less than 1/3 ?

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Q: What is the probability distribution of X when X∼B(1,125)? Group of answer choices P(X=0)=0.75…

A: From the provided information, Number of trials (n) = 1 Probability of successes (p) = 0.25

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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!