For the following joint probability mass function: |y f(x,y) |-1 -2 1/8 |-0.5 -1 1/4 0.5 1 1/2 1 2 1/8 What is P(X<0.6, Y<1.6) ?

Q: d) Consider the continuous random variable with probability density function (1-t. for-1≤t ≤0 11-t.…

A: The probability density function of tf(t)=1+t.          for -1≤t≤0       1-t.             for…

Q: (a) What is the probability that the sample consists of balls of three different colours? (b) What…

A:

Q: The velocity v of an object of mass m = 5 Kg is a random variable with probability density function…

A: We have to find correct answer..

Q: Let the Probability Mass Function as follows: f(-1)=0.2, f(2)=0.3, f(3)=0.35 and f(0)=??, Then F(2)=…

A: The given probability mass function is as follows f(-1) = 0.2 f(2) = 0.3 f(3) = 0.35 We have to find…

Q: What is the value if the constant c for p(x) to qualify as a probability mass function?…

A: Solution: From the given information, the probability mass function of X is

Q: The thickness of a wooden shelf in mm, has probability density function             f(x) = {0.75 –…

A: Given probability density functionf(x)=0.75-0.75(x-5)2  4≤x≤60otherwise 1.The mean of the…

Q: The amount of electricity consumed (in kWh) on a randomly chosen day in a warenouse Can probability…

A: Given that  Probability density function f(x) f(x)=30/x2     , 25&lt;x&lt;150           0…

Q: The velocity of a particle in a gas is a random variable X with probability distribution fx(x) =…

A:

Q: Is f(x) a legitimate probability mass function? (1 – p)"='p =p+ (1 – p)p + (1 – p)²p+ • …· ² 1 x=1

A: We know that to be a legitimate mass function we must have 0≤f(x)≤1 for all x.  And the sum of all…

Q: Figure 1 shows the piecewise function (I), (II), (III) and (IV) for cumulative distribution function…

A: We have to construct the probability density function f(x)

Q: The relationship between probability distribution function F(x) and the probability density function…

A: To find whether the given statement is true or false:

Q: For the probability distribution, find d. P(y = 6) e. f(y = 4) f. f(y= 6) g. F(y = 5.5) h. F(4) f.…

A: Since total probability is always 1:P(Y=−2)+P(Y=−1)+P(Y=0)+P(Y=1)+P(Y=2)=1

Q: The probability density function fX (x) of the random variable X fX(x) =(  4x3            0 1/3)…

A: Given the probability density function of the random variable X is fXx=4x3      0&lt;x≤1  0…

Q: f (y) = a (b– y), 0 < y < b, and 0 elsewhere. If the mean of the distribution is .2, find the values…

A: The density function of Y is given by, f(y) =  a (b-y) , 0&lt;y&lt;b Hence, ∫0ba(b-y) dy = 1…

Q: Consider the continuous probability density function defined by y= 0.25 on -2.6 -2.2) =  P(X <…

A: The probability density function is:.

Q: can you explain how you get P(X=x)xP(Y=y). is this the joint probability mass function?

A: It is given that,  X~ Poisson(ϕ) and Y~ Poisson (ϕ)

Q: The diameter of a particle of contamination (in micrometers) is modeled with the probability density…

A:

Q: The diameter of metal cylinder has a probability density function of f(x)=1.5-6(x-50.0)2 [mm] 500…

A:

Q: Consider the probability density function if x -4 + (x+4)³ Find the median. Select one:

A: Given information: fx=1x+43 if x≥-4+12 Consider, Fx=∫-4+12xftdt       =∫-4+12x1x+43dx      =-12x+42…

Q: What should be the value of k for f(x) to be able to be a probability density function? f(x)=(2kx)/6…

A: Given:fx=2kx6=kx3                             ;0&lt;x&lt;8

Q: 1. Find the value of c that will make the pdf valid. 2. Derive its corresponding distribution…

A:

Q: X F(x) 0 0 10 2 C 3 0.5

A: Given  x 0 2 3 F(x) 0 C 0.5

Q: Which statements below are true for a probability distribution function (pdf), f(x)?     The total…

A: The total area under f(x) is equal to 1. f(x) is a probability f(x) is non-negative

Q: Q1. The cumulative distribution function of the random variable X is F(x) = 0, (+1)², 1- (1-2)², 1,…

A: Let X be the random variable having cumulative distribution function

Q: Consider the probability density function f(x) = 1.5x² for-1 ≤x≤ 1. What is P(x > 0)? a. 0 b. 0.125…

A: It is given that  The probability density function of continuous random variable X is  f(x) = 1.5x2,…

Q: Q2. The probability density function of X is as follows. f(x) = 2 - 2x, for x = [0, 1] Which one of…

A: The probability density function of X is given by,We need to find,

Q: Find the conditional probability density function of Y given X? pte: If the answer is (9+1) write it…

A: Solution

Q: Let f(t) be the probability density function for the time it takes you to drive to school in the…

A: It is given that f(t) is the pdf for the time it takes to drive to school, where t is the number of…

Q: Daily total solar radiation for a specified location in Florida in October has probability density…

A:

Q: The diameter of a particle of contamination (in micrometers) is modeled with the probability density…

A: Given,f(x)=2x3   ;  x&gt;1

Q: Suppose Y Uniform(01,02) where the parameters 01 and 02 take the values 1 and 5 respectively.…

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!