Q4- Let X be a random variable with probability density function Scx² + x 0< x<1 f(x) = {e* 0.w for some constant c> 0. What is the value of c?

Q: 10) Let f(x) by the probability density function of some continuous random variable. Explain why it…

A: If f(x) denotes the probability density function of some continuous random variable where x goes to…

Q: A continuous random variable X has the probability density function 2 -(9 – x) if 0 < x < 9 81 f(x)…

A:

Q: 6. Determine the value of c that makes the function f(x, y) = cxy a joint probability density…

A: Given,f(x,y)=cxy  ;  0&lt;x&lt;2 , 0&lt;y&lt;x

Q: b. Let X be a continuous random variable with probability density function for 0 <x < 1 for 1 <x< 3…

A: Givenf(x)=a     for 0≤x≤1b    for 1≤x≤30    otherwise

Q: Let X be a random variable with probability density function, What is Var(X)? f(x) = cx(5-x) for…

A:

Q: A continuous random variable has the probability density function of f(x)=0.0118x and the interval…

A:

Q: What is the moment generating function of the random variable X whose probability density function…

A: Given X~exp(1)

Q: Find the expected values of continuous random variables with probability density function, f(x)=…

A:

Q: b. Let X be a continuous random variable with following probability density function as f(x) = 6x(1–…

A: Given information:  X is a continuous random variable with following probability density function…

Q: Let X be a random variable with the probability density function. f(x) : 20 for x = 1,2,3, 4, ..., 0…

A:

Q: 11. Consider the random variable X with probability density function fx (x) = a/a -1<r < 1, where a…

A:

Q: 2) Let X be a continuous random variable with Probability density function f(x) = x + 0<x<1…

A:

Q: Consider random variable X that is exponentially distributed with E(X) = 2. Select the probability…

A:

Q: Q4. A random variable X takes values between-2 and 3 with a probability density function 15 64 + cx,…

A:

Q: Q2 Let the probability density function of a random variable Y be y, f(y) = 2-y, 0≤x≤1 1<x<2…

A: The given pdf of random variable Y is, fy=y,              0≤y&lt;12-y,        1≤y&lt;20,…

Q: Two Random Variables X And Y Have The Following Joint Probability Density Function (PDF) fxx (x,y) =…

A:

Q: Q3-Let X be a continuous random variable whose probability density function is .3 f(x) : 4 for an…

A:

Q: Q2 Let the probability density function of a random variable Y be 0≤x≤ 1 f (y) = = = {2² y, {2-y, 0,…

A: Given

Q: Let the probability density function of a random variable X be 630r (1 – 1)* if (0 <I<1 f(z) = .…

A: Given

Q: Consider a probability density function for a random variable X, defined by for 1 < x < 3 f(x) = 16…

A: The probability distribution of a discrete and continuous random variable is known by the name as…

Q: Let X be a random variable with probability density function 3 -x², -1 < x < 1 2 Which of the…

A:

Q: A continuous random variable has the probability density function f(x) = 1/8 for 0 ≤ x ≤ 8. What is…

A: Expected value of a continuous random variable:Continuous random variable:If the variable X takes…

Q: 1) The probability density function of the weight in kilogram of passenger baggage received by an…

A: Solution

Q: Q2 Let the probability density function of a random variable Y be 0 < x < 1 f(y) = = {2 y, 2-y, 0,…

A: We have given the following about the probability density function of a random variable.

Q: A random variable X has a distribution function given by: (0, F(x)= {k(x-1)*, 13 1. Determine the…

A: Probability is the chances of occurrence of an event. The probability density function f(x) gives…

Q: A continuous random variable X has the probability density function if 0 < x < 8 { (8 – x) 32 f(x) =…

A:

Q: 3. If a random variable has the probability density for x>0 2e-2* f(x) = for x <0 Find the…

A:

Q: Let 0 be a parameter. Show that the family of functions fo(x) = x >0 à probability density function.…

A: 4. Condition for probability density function ∫f(x)=1. consider, ∫0∞f(x)dx=∫0∞θe-θxx2dx…

Q: a) A random variable X has an exponential distribution with probability density function given by…

A:

Q: 12. The continuous random variable X has probability density function S2xe, >0 fx(x) = 0, %3D…

A:

Q: 3. Consider the probability density function of a continuous random variable X f(x) = { − ³x + 1≤x≤4…

A:

Q: 10. The probability density function for a continuous random variable X has the form, find the value…

A: For the given pdf Find c= ?

Q: probability density function for (X, Y) is as follows. Compute the probability that neither railroad…

A: Here given joint pdf  Using integration finds the required probability

Q: 4. The lifetime in hours of an electronic gadget is a random variable having a probability density…

A:

Q: If X has probability density function f(x) = %3D X/32 on [0, 8], find the expected value and the…

A:

Q: B) The probability density function for the random variable X is given by 0<x<3 f(x) ={(25 – x²), 0,…

A: Given function is,  f(x)=x2, 0&lt;x&lt;3(25-x2), 3≤x&lt;60, otherwise

Q: A continuous random variable has probability density function given by K(2x-3);1&lt;x2 Find k if…

A:

Q: Let X be a random variable with probability density function f(x) = 3*123*x4 for x> 12. Determine…

A: Given : Let X be a random variable with probability density function f(x) = 3*123*x-4 for x &gt; 12.…

Q: The probability density function of a random variable is kx3 f(x) = if 0 <x< 2 V25 – x2 = 0…

A:

Q: Suppose lifetime of a particular type of old mobile, X, can be modelled by the probability density…

A:

Q: (b) The continuous random variable X has the probability density function 3 f(x) =x² for interval…

A: Solution

Q: 3. Suppose X and Y have joint probability density function f(x,y) = {"0. 0 < x< 1,0 < y <1- x…

A:

Q: The continuous random variable X has the probability density function (pdf) given by: [k-5+x S(x) =…

A:

Q: A continuous random variable, X, has the following probability density function. k cos f(x) = { for…

A: Given: The distribution of X is  fx=k×cosπx2     0≤x≤1

Q: 3. Let X and Y be two independent random variables with identical probability density function given…

A: Introduction : Here, X and Y are identically and independently distributed exponential random…

Q: 6. Determine the value of c that makes the function f (x, y) = cxy a joint probability density…

A:

Q: Let X be a random variable with probability density function, What is EX? f(x) = x(5-x) for 0≤x≤5 0…

A:

Q: 1. Consider a random variable X with probability density function given as: 0 if x < 0, 1 if 0 ≤ x ≤…

A:

Q: (8) The moment generating function of the random variable X having the probability density function…

A: Since , the probability density function is given by ,  Our aim is to find the moment generating…

Q: Esample 27 : If a random variable has the probability density function k(x2 –1),-1< x<3 f(x)= - [0,…

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!