Let f(t) be the probability density function for the time it takes you to drive to school in the morning, where t is measured in minutes. Express the following probabilities as integrals. (If you need to use co or -oo, enter INFINITY or -INFINITY, respectively.) (a) the probability that you drive to school less than 50 minutes f(t) dt (b) the probability that it takes you more than a quarter of an hour to get to school f(t) dt

Q: Let X be the total amount saved in dollars at the cash register. The pdf of X is given by: Value of…

A: Formula : E(X) = ΣX *P(X)

Q: s(VE + E dx

A: We want to integrate the given function.

Q: Value of k in the following pdf is x: 1 2 f(x): k k 2k а. 1/3 b. 1/2 c. 1/4 d. None of these

A:

Q: 2- |In (=) dx.

A: ∫01ln 1x     dx

Q: Va -, -dx Va + x Evaluate (i)

A: on doing integration we get

Q: 10 Evaluate , 11 f(x)dx given that f(x)dx = 4 and Sa f(x) dx = -2. -3 10

A:

Q: Find S xJ3(x)d

A:

Q: Consider the Prelec function w(p) = e−1.7(− ln p)0.75 . Consider only interior fixed points (so…

A: A two parameters probability weighting function is of the form: wp=exp-β- ln pα             α>0,…

Q: Consider the probability distribution function (PDF) f(x) = Ax sin x, for 0 <xs N (a) Consider…

A: a) Given that  The value of A is calculated below:                ∫0πf(x)dx=1…

Q: Let r1 and r2 denote the annual returns of stocks 1 and 2. Assume that (r1, r2) ~ BVN((0.08, 0.05?),…

A: Given  r1, r2~BVN0.08, 0.052, 0.05, 0.152, -0.5

Q: 14 ounces. 34. If you are really bad at darts, then the PDF for the distance x (in inches) that your…

A:

Q: P(A|B)=0.2, P(A|B')=0.3 ve P(B)=0.8 , P(AUB)=?

A:

Q: What is the mean (E[X]) of the following statistical function? f(x)=c*(x)^9 from 0 to 9 and f(x)=0…

A:

Q: S Vx In(x) dx.

A: The objective is to find the integration.

Q: Let [ 13.5 f(x) dx = 8, 45 f (a) f(x) dx = 3 J4.5 9 (b) (5f(x) - 2) dx = J4. f(x) dx = 3, and Enter…

A: Given : ∫013.5 f(x) dx=8,∫04.5 f(x) dx=3 and ∫913.5 f(x) dx=2. To find: (a) ∫4.59 f(x) dx= (b) ∫4.59…

Q: -5x Integrate x² e

A: We have to find

Q: Evaluate f(x³ -x + 1) dx a. 0.250 b. 0.500 c. 0.625 d. 0.750 e. NONE OF THE ABOVE

A:

Q: Graph the function.f(x) = int(x + 3)

A: The objective of the question is to graph the function f(x) = int(x + 3). Here, 'int' denotes the…

Q: X is exponentially distributed with a mean of unity. What is the pdf of Y=1-exp(-X)? Use the 440 40…

A: Given,

Q: st ар хи पा S

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Q: Consider the probability distribution function S(x) = Ar sin z, for 0SIST (a) Consider whether f is…

A:

Q: Find and explain the error in the following 1 (In |x – 3|) |. - х — 3 = In |6 – 3| – In |0 – 3| =…

A:

Q: (b) Pr[X > 0.6n] < 0.85. Let X be the number of HEADS after n fair coin tosses. Show that

A:

Q: Let X have the pdf f(x)= ce-2(x-1)", -0<x<. What is the value of c?. Select one: a. 0.4358 b. 0.7979…

A:

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!