Given the probability density function of X : -1sxs0 2 S« (x)=< x20 a. Find the probability density function of Y , f,(y), given Y = X². b. Check the answer to a. by verifying that [ f,(y)dy =1 .

Q: 2. Identify the probability density function, then find the mean and variance without integrating.…

A:

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 random variable X has the probability density function 1 1 f(x) = n x2 + 1' then the probability…

A: Here we've to find, P(1/3&lt;X2&lt;1) We can write it, P(√1/3&lt;X&lt;1)

Q: Let X be a random variable uniformly distributed over the interval [2, 3]. (a) Find the probability…

A:

Q: . Find the probability density function of y

A: Given: Here a point is X selected at random from the interval (0,1) then the another point is…

Q: Suppose X~Uniform (0,1), and Y = -ln (1-x). (a). Find the probability density function of Y

A: Given that X follows Uniform distribution with (0, 1). Y=-ln1-X a) Consider, the cumulative…

Q: Let X and Y has joint probability density function f(X, Y) = 81 - , 0 <x< 3, 0 <y< 3. Find E(X).

A: The joint probability density function is, fX,Y=x2y281,0&lt;x&lt;3,0&lt;y&lt;3

Q: The exponential probability density function is f(y, 2)= he- for y, 120 Show that the exponential…

A:

Q: The probability density function of a known distribution is 1 f(u10) = T O exp (-), y>0, r(v) where…

A: The Gamma distribution is defined as follows :

Q: Determine the value of c for which the function below will be a probability density functi So(8x' -…

A: Here given thatf(x)=c8x3-x4   ; 0≤x≤80                    ; other

Q: If the probability density function of X is : f(x) = e-x (1+e*)2 en what is the probability density…

A: It is an important part of statistics. It is widely used.

Q: Let X be a continuous random variable with probability density function f(x) = 2(1-x),  0<=x <= 1.…

A: Given: f(x) = 2(1-x),   0≤x≤1 Y = 2X-1 To find: pdf of Y = ?

Q: ~ The time to decay of an atom in a radioactive substance is a random variable X. The law of…

A: Given:    The law of radioactive decay states that if N atoms arepresent at time t = 0, then N f…

Q: fxlx,y) = x2y is a joint probability density function over the range 0<x<2 and 0<y<3 12 Find the…

A:

Q: Suppose that X takes values between 0 and 1 and has probability density function x2 (2x +). If Y…

A: The arithmetic mean of squares of deviations taken from the arithmetic mean is called as…

Q: fx1,x₂(x1, x₂) = 0, otherwise. What is the joint probability density function fy₁,Y₂ of Y₁ = X₁/X2…

A:

Q: 2. Let X be a continuous random variable with probability density function (pdf) [3x² 0<x<1…

A: f(x)=3x2.       0&lt;x&lt;1 0.               OtherwiseWe have to find the probability density…

Q: Suppose that X ~ Unif[0, 1] and let Y = e^X. (a) Find the cumulative distribution function of Y .(b)…

A: In particular, the cdf and pdf of X is, Since, ex is an increasing function of x and Rx = [0, 1],…

Q: A random variable X is uniformly distributed in the interval (-л/2, π/2). Xis transformed to a new…

A:

Q: re x is the life length of transistor I ar . The joint probability density function 2e-(x+2) x 20, y…

A: The conditional probability is,  The formula to compute density function of y is,

Q: Let X be a continuous variable with probability density function /(x) cx' defined for 0sxs1, where c…

A: We know that the total probability is always 1.  That means: ∫01f(x)dx=1

Q: The lifetime of a machine part has a continuous distribution on the interval (0,45) months with…

A: Given that  f(x) is proportional to (4+x)-2. So, f(x)=k(4+x)-2 , 0&lt;x&lt;45 Total probability must…

Q: What is the joint probability density function f₁,2 of Y₁ = X₁/X₂ and Y₂ = X₂?

A: We will use Jacobian method of transformation to find the joint probability of Y1 and Y2.

Q: While taking a walk along the road where you live, you accidentally drop your glove, but you don't…

A: According to the information provided in the question, the  probability density for dropping the…

Q: Determine the conditional probability distribution of Y given that X = 2. Where the joint…

A:

Q: Sex² f(x)=cis a probability density function? 0.111 (2 c) 0.5 / The value of the constant, which…

A:

Q: Consider the probability density function fx (x) = a e-b lel where X is the ran variable which…

A:

Q: Suppose that the probability density function of the length of computer cables is f (x) = 2x/(32)…

A: Let X be the continuous random variable which denotes the length of the computer cables.The…

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!