f the random variable X follows the uniform distribution U= (0,1) What is the distribution of the random variable Y= -2lnX. Show its limits.

Q: What is the probability that a leatherback turtle will weight more than 1000 pounds

A: Given that X follows N(mean = 760, SD = 98), then Z = (X - mean)/SD follows N(0,1)

Q: Show that the t-distribution with r = 1 degree of freedom and the Cauchydistribution are the same.

A: We have to prove that the t distribution with r=1 degree of freedom and the Cauchy distribution are…

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Q: When sigma is KNOWN and n is less than 30, we use t-distribution True or false?

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Q: If Y Poisson(2) and Z Poisson(3) are independent, what is distribution of W = Y + Z?

A: Solution: Given  Y~Poisson(2)    and  Z~Poisson(3)   Y and Z are independent random variable

Q: If X~beta(3,2) is independent of Y~beta(3,4), what is the distribution of X+Y

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Q: What is the distribution of X? 1) Out of the 38 pizzas that you try, how many would you expect to…

A: Let p be the probability of you liking the pizza. Given that p = 0.08

Q: The graph of a continuous probability distribution cannot have y-values larger than 1.

A: Given that   The graph of a continuous probability distribution cannot have y-values larger than 1.…

Q: For a highway, the car's speed has a uniform distribution [50,90]. Cars are stopped if speed X is…

A:

Q: X ~ N(60, 14). Suppose that you form random samples of 25 from this distribution. Let X be the…

A: It is given that: X~N60, 14 Sample sizen=25

Q: Suppose the length of a music jingle has constant probability for all lengths between 60 and 75…

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Q: The repair times of smart phones in a repair shop are independent random variables with the same…

A:

Q: The number of particles emitted at a radio frequency follows Poisson distribution with an average…

A: Given data  λ = 120 particles per hour   = 12060 particles per minute   = 2 particles per minute

Q: If(x,y)-N(0-11,4,0.5),the marginal distribution of X~ Y₂

A:

Q: Let X ~ I(2,8). Find the distribution of Y = 2x.

A:

Q: If the distribution function f(q) for some physical property q is even, it follows that q = 0. Does…

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Q: A researcher claims that the number of homicide crimes by season is uniformly distributed. To test…

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Q: If X is a random variable with any continuous distribution, explain why P(X<x)=P(X≤ x)

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Q: Assume that the amount of weight that male college students gain during their freshman year are…

A: NNote: this probability value calculated from standard normal distribution table

Q: Which distribution's height begins low, increases until the middle, and then decreases such that it…

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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!