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In Problems 25 and 26, graph f, and show that f satisfies the first two conditions for a probability density function.
25.
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Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)
- solve only 4 and 5 plzarrow_forward6. Roughly, speaking, we can use probability density functions to model the likelihood of an event occurring. Formally, a probability density function on (-x, o0) is a function f such that f(r) 20 and (2) = = 1. (a) Determine which of the following functions are probability density functions on the (-x0, 00). fr-1 00 (b) We can also use probability density functions to find the erpected value of the outcomes of the event - if we repeated a probability experiment many times, the expected value will equal the average of the outcomes of the experiment. (e.g. rf(x) dr yields the expected value for a density f(r) with domain on the real numbers.) Find the expected value for one of the valid probability densities above.arrow_forwardpart D E needarrow_forward
- 1arrow_forward3. If a random variable has the probability density |2e-2* f (x) = - for x >0 for x <0 Find the probability that it will take on a value between 0.5 and 1.arrow_forwardIn 1938, a physicist named Frank Benford discovered that the number 1 appears in the first digit of random data more often than the number 2, the number 2 more often than the number 3 and so on. In general, the probability of occurrence of the first digit of a number can be written in the form of a probability function x + 1 P(X = x) = log. X a. Prove it P(X = x) = log ) untuk x = 1,2,3,4...,9 x+1 X x = 1,2,3,4..., 9 is a probability mass function 2 b. Find the cumulative distribution function of X!arrow_forward
- 6. Roughly, speaking, we can use probability density functions to model the likelihood of an event occurring. Formally, a probability density function on (-oo, 00) is a function f such that f (x) >0 and | f (x) = 1. (a) Determine which of the following functions are probability density functions on the (-0, 00). x-1 00 (b) We can also use probability density functions to find the expected value of the outcomes of the event if we repeated a probability experiment many times, the expected value will equal the average of the outcomes of the experiment. (e.g. xf(x) dr yields the expected value for a density f(x) with domain on the real numbers.) Find the expected value for one of the valid probability densities above.arrow_forward2. The number of minutes a flight from Phoenix to Tucson is early or late is a random variable whose 1 (36– x*) for-6arrow_forward(1) Let X b(16,- 5,-) find E(4- 3x) and distribution function.arrow_forward7. Let X be a continuous random variable with probability density function given by Se-(2-z0) f (x) = x > x0 x < xo Find E(X).arrow_forwardB- Show that if the following function be probability function: for 0arrow_forward. Find each probability.(a) X ∼ Gaussian (0, 3). Find P[X > 4.5].(b) Y ∼ Gaussian (50, 10). Find P[X < 75]arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_iosRecommended textbooks for you
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