Let X be a continuous random variable with density function: E(3x + 1) 0 < x < 1 f(x) = }5 0, otherwise Then P(X<1/3) is equal to: O 1/5 O 4/9 O 5/9 4/3

Q: let x be a continuous random variable with probability density funct Find f(x) = 0, -3x 0<x<3 O.W…

A: Formula  Used: If X be a continuous random variable, -∞&lt;X&lt;∞ f(x)  is called probability…

Q: If X and Y are random variables having the joint density function f(x,y) = (6-x-y), 0<x<2, 2<y<4.…

A: Here Given joint pdf of two random variable x and y f(x,y) = 186-x-y , 0&lt;x&lt;2, 2&lt;y&lt;4

Q: If X is uniformly distributed over (-1,1), find P(IX| > а. b. Density function of the random…

A: The given information is X~U[-1,1] a.…

Q: X is continuous random variable with probability density function px +1,0 k) =

A: (a) Here,   Hence the value of p is -1.   Since we can calculate q as follows: Hence the value of…

Q: A continuous random variable X that can assume any value between X = 2 and X = 5 has a density…

A:

Q: f X is a continuous random variable with a density that is symmetric about some point, ξ , show that…

A: Introduction: Given that X is a continuous random variable with a density that is symmetric about…

Q: Let X be a continuous random variable with density function f(x) = {2x    if x ∈ [0,1]           {0…

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

Q: Let x be a random variable defined by density function fx=3x^2 define less than equal to 1 and great…

A:

Q: Let X be a continuous random variable with a probability density function (6-3e)x2 + eš 0<x<1 f(x) =…

A:

Q: Let X be a random variable with density function -1< x < 2, elsewhere. 2/3, f(x) = 0,

A:

Q: Let X be a continuous random variable with a density function: 5|x| k -15x<1 f(x) = 3 0, otherwise…

A: Given: fx=k5x3,        -1≤x≤1       =0,                   otherwise Given function is a density…

Q: b) Suppose that X is a random variable with the probability density function given f(x) = {201₁ Find…

A:

Q: Let X be a continuous random variable with density function S 6x(1 – x) for 0 ) Calculate P

A:

Q: Let X and Y be continuous random variables with a joint probability density function (pdf) of the…

A: Given X and Y are continuous random variables with a joint probability density function (pdf) of the…

Q: is a probability - Find k such that f(x) = {kx(1 – x)² for 0 <x<1 %3D otherwise density function for…

A: The total probability must be 1. So,

Q: Let X and Y be two continuous random variables with joint probability density function given by:…

A: Cov(X,Y)=E(XY)-E(X)E(X)

Q: If p(x, y) is the joint probability density function of randomvariables X and Y, what does the…

A: Probability density function p(x, y) is given.

Q: Let X be a continuous random variable with probability density function 1 f (x) = 7(1+x² ) Define Y…

A: The mean of Y is given by: μ= E(Y) = E1X It is known that,  E1X = ∫-∞∞1xf(x) dx

Q: Let X,Y be continuous random variables with joint density function if 0 < x < 1,x < y < 1 f (x, y) =…

A:

Q: Let X be a continuous random variable with a density function: 3|x| k f(x) = - 25xS2 0, otherwise…

A: f(x) = k 3x2   , -2⩽x⩽2  0          ,   otherwisef(x) = k X -3x2   , -2⩽x⩽2  k X 3x2          ,…

Q: Let X be a continuous random variable where the density function is given by: (1x) 0 if-3<x<3…

A: Given information: fx=x9, -3&lt;x&lt;30 otherwise    =-x9, -3&lt;x&lt;0x9, 0&lt;x&lt;3Consider,

Q: Let X and Y be continuous random variables with a joint probability density function (pdf) of the…

A: The value of k will be obtained as given below: The joint pdf of  X and Y is 2(x+y),…

Q: The probability density function fx) of a continuous random variable x is defined by A 5sxS 10 f(x)…

A:

Q: Let X be a continuous random variable with probability density function given by ƒ(x)=Kx³ if x21,…

A:

Q: Let X be a continuous random variable with density functionf(x) = 3x^-4, x ≥ 1. Compute E(X ) and…

A: Given function is, fx=3x-4, x≥1 Now, Ex is computed as follows:…

Q: (a) Let X be a random variable of the continuous type with probability density function f(x). which…

A: X is a random variable of continuos type with probability density function  which is defined over…

Q: Let f(x) is density function of continuous random variable x then the (expected value E(x E&) = […

A: Given that, X is a continuous random variable, and f(x) be the p.d.f. of X.

Q: Let (X, Y) be two jointly continuous random variables such that the conditional prob- ability…

A: # conditional pdf of y/x is given and x follow uniform (-1,1)  Then to find Expected value of y ??

Q: Let X and Y be continuous random variables with joint probability density function given by 4.…

A: To find the covariance of X and Y we need to find the marginal distribution of X and Y first.

Q: Let X be a continuous random variable with density function: (ke* if x>0 f(x) = otherwise Then E(X)…

A:

Q: Let X be a continuous random variable with density function: (3x + 1) 0 < x< 1 f(x) = otherwise Then…

A:

Q: Let X be a continuous random variable with density function fx(x)= (a) Find P(X> 10). (b) Find the…

A: Solution Given

Q: Let X1 have the density function .3 4x;, f,(x,) = 0, 0<x1 <1, otherwise. If the conditional…

A: Given, The density function of X1 as: Conditional distribution of X2 given X1=x1 is:

Q: The density function of a continuous Random variable X is fx (x) = ax for 0sx <I for 1sx <2 for 2 sx…

A:

Q: Let (X; Y) be a continuous random vector with joint probability density function 0.5 -1sx 0) equals

A: Given, Let (X; Y) be a continuous random vector with joint probability density funcion :   fX,Y…

Q: Suppose that the joint density function of random variables X₁₂ and X₂ is given by >-£/. 0, f(x₁,…

A: i)

Q: Let X be a continuous random variable with density function 2x-2 for x > 2 f(x) = otherwise…

A: We have to find the pdf of y which is function of x.

Q: Let X be a RV with the following probability density function f (æ) = { (6+1) xº, 0<x<1 0, f (x): (0…

A:

Q: Let X be a continuous random variable with density function f(x) =2 cx² |x| <1 elsewise Then c is…

A:

Q: A zero-mean stationary Gaussian random process X(t) has power spectral density S_x(f). Determine the…

A: Given that : A zero-mean stationary Gaussian random process X(t) has power spectral density Sxf. The…

Q: Let X and Y be two continuous random variables with joint probability density function given by:…

A: We know that  COV = E( XY) - E(X)E(Y)

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

A:

Q: Let X1, X2, X6 be an ii.d. random sample where each X; is a continuous random variable with…

A: We know, fx=e-x-θ  ,  x&gt;θ And, X1, X2, ... ,X6 are IID random variables

Q: Let X be a continuous random variable with a density function: 3|x| k 2 - 2<x<2 f (x) = 0, otherwise…

A: A continuous random variable has infinite values and the number of values are not countable. The…

Q: Let X and Y be continuous random variables with a joint probability density function (pdf) of the…

A: Find cdf of x and y

Q: Let X be a continuous random variable with density function: (3x +1) 0<x<1 f(x) = 5 0, %3D otherwise…

A: We've to find, P(X&lt;=1/3) = integration |01/3 f(x) dx

Q: 8. If X is uniformly distributed over (–1,1), find a. P(\X|>;) b. Density function of the random…

A: Solution

Q: Let X be a continuous random variable with a probability density function ((6-3e)x² + ex 0 0<x< 1…

A:

Q: Let X be a random variable with density function k+1 x? 0<x <1 fx =. otherwise Find the moment…

A: Given, The pdf fx=k+1x20&lt;x&lt;10otherwise

Q: Find the value of c so that ƒ(x) = csqrt(x)(1 - x) is a probability density function for the random…

A: Write the given expression and simplify it using the definition of probability density function.

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!