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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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- solve only 4 and 5 plzarrow_forward11. The distribution function of a random variable X is given by -e-x² X>0 otherwise F(x)= Find the probability density function.arrow_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_forward
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- In 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_forward6. 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_forward7. If a random variable has the probability density function -1≤x≤3 otherwise f(x)=k(x²-1) =0arrow_forward
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