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a) Find P(1<x<2.25)
b) Find the cumulative distribution
by using CDF find P(1.25<x<1.5)
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- 2. Consider the experiment of rolling a die until a "6" appears. Let X be the number of rolls needed. Plot the Cumulative distribution function Fx(x) of X. Describe what it means for a function to be right-continuous. You are encouraged to use a computer program to plot this, although it is acceptable that you use rulers and pencils. (You don't need to plot the whole function because the possible values could be ar- bitrary large. Try to plot from 0 to the value that you think it shows the major trend.)1. or a cumulative distribution funetion (cdf). Decide if the function graphed below is a probability density function (pdf) 2c 4 8.Pregnancy Length in a Population of New Mothers Assume a member is selected at random from the population represented by the graph. Find the probability that the member selected at random is from the shaded region of the graph. Assume the variable x is normally distributed. 280The following function is a cumulative distribution function. x < -10 0.1510An actuary models loss amounts under a insurance policy using the Pareto distribu- tion. The cdf of the Pareto distribution Suppose that 0 = 1400 and a = 1.6. What is the expected is F(x) = 1 (0/(x+0))ª. payment under a claim given that the policy has a deductible of 350 and a limit of 1300?Suppose a traveler’s location is uniformly distributed inside a circle with a radius 2. Let X be the distance between the traveler and the center of the circle.Determine the cumulative distribution function of X.if x 20 Find the following: P(X > 22) =| The cumulative distribution function of X: if x 20 The probability that at least one out of 8 devices of this type will function for at least 29 months:Cumulative probability tables for the Poisson distribution indicate that for µ = 2.5, Pr [R ≤ 6] = 0.986 and Pr [R ≤ 4] = 0.891. Use these figures to calculate Pr [R = 5 or 6]. Check using basic relations.b) Sketch the probability mass function and the cumulative distribution function of X (c) Consider a random sample of 6 parcels. If Y is the number of parcels taking longer than 1 day to arrive, write down the distribution of Y and its mean and variance.Recommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSONA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON