The total area under the probability of density function is always pot above
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- According to the figure, demonstrate the density function of the triangular distribution, taking into account that the area of the triangle is 1.Let the radius of a circle be a random variable X with density function f(x) = 1 for 0 < x < 1 and f(x) = 0 otherwise. What is the probability density of the area of the circle?Suppose random variable X has a density function f ( x ) = { 2 /x 2 , 1 ≤ x ≤ 2 0 , o t h e r w i s e . Then E[X4] =?
- The amount of weight required to break a certain brand of twine has a normal density function, with μ = 43 kilograms and σ = 1.5 kilograms. Find the probability that the breaking weight of a piece of the twine is less than 40 kilograms.Suppose the amount of time (x) to complete an exam is uniform between 30 and 60 minutes. A) Draw the density curve for for the unknown height (h) B) What is the probability that the exam takes between 30 and 35 minutes or 55 and 60 minutes? Enter your answer as a fraction.The experiment is to toss two balls into four boxes in such a way that each ball is equally likelyto fall in any box. Let X denote the number of balls in the first box.a. What is the CDF of X?b. What is the density function of X?
- The experiment is to toss two balls into four boxes in such a way that each ball is equally likely to fall in any box. Let X denote the number of balls in the first box.a. What is the CDF of X?b. What is the density function of X?From the density of the image below what is the probability that x is at least 0.34 ?Suppose the random variables X and Y have joint probability density function f(x,y) given by: (image)Find: P(X < Y) = fX|Y=y (x)
- The life (in years) of a laptop battery has a probability density function defined by P(x)=12e−x/2P(x)=12e-x/2for x in [0,∞)[0,∞). Find the probability that a randomly selected laptop battery will last between 3 and 8 years?Suppose that X ~ Unif[0, 1] and let Y = e^X. (a) Find the cumulative distribution function of Y .(b) Find the probability density function of Y .If the joint density of X and Y is given byf(x, y) =⎧⎨⎩e−(x+y) for x > 0, y > 00 elsewhere and Z = X + Y2 , find the probability density of Z by thedistribution function technique.
