Let X be a random variable with probability density function   (a) What is the value of c? (b) What is the cumulative distribution function of X?

Q: What is a probability density function?

A: The density of a continuous random variable lying between a certain range of values is called the…

Q: The probability density of a random variable X is given in the figure below.     From this…

A: From the given figure, we can see that the X~U(0,2) i.e. f(x) =1/2 ; 0<x<2

Q: What are the two properties of a probability density function?

A: Let fx be the Probability density function.

Q: Let X be a random variable with probability density function f(x) = c(8x-x^2) if 0<x<8 otherwise…

A: Given: x is a random variable with probability density function. f(x)=c(8x-x2)      if0&lt;x&lt;80…

Q: Let the probability density function of the random variable X be given as (pdf). Event A = | X - b |…

A: From the given information,  Pdf of the random variable X is,  fXx=c1-x2    -a≤x≤a0…

Q: The probability density of a random variable X is given in the figure below. 0. 1 From this density,…

A: From the graph, we see that X is a continuous uniform distribution between 0 to 2.

Q: let x be a random variable with probability density function f(x)={ c ( 1-x^2)  -1<x<1           0…

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

Q: What is a probability density function? What is the probability thata continuous random variable has…

A: Given: Probability density function. Objective is to defined the probability density function and…

Q: Please see attached image.

A: Given density function

Q: The probability density function for continuous random variable, x, is given above. P(x P(x = 1.5) =

A: We have to find P(X = 1.5) using the probability density function of X.

Q: Consider two continuous random variables X and Y characterized by the following joint probability…

A: a) From the given information, Condition for valid probability density function is,  Consider,

Q: Find the probability density function of X.

A: The pdf of X can be obtained by differentiating the cumulative distribution function F(x)

Q: Let X be a random variable with probability density function f (x) = } 0, otherwise a. What is the…

A: Given function is f(x)={c(1-x2)             -1&lt;x&lt;10                          otherwise

Q: Determine the probability density function for the cumulative distribution function shown below.

A: Given:  cdf of random variable x is   F(x) is given then find probability density function of x ??

Q: A cumulative distribution function can be used to find the probability density function of a…

A: TRUE ,cumulative distribution function used to find probability density function of discrete RANDOM…

Q: The lifetime of a certain mobile can be represented by probability density function of a random…

A: Part (a) Use the formula ∫-∞∞Ay2e-y/4dy=1 to calculate the value of A.…

Q: A continuous random variable X has the probability density function  f(x) = (4-x)/8, 0 ≤ x ≤ 4. Find…

A: The probability density function for a continuous random variable X is, fx=4-x8,     0≤x≤4

Q: Is it a valid probability density function?

A:

Q: Let X be a random variable from the Pareto distribution with probability density function {(=10) = {…

A: Solution

Q: The probability density function of random variable X is given as: if 0 < x < 2 8 f(x) = 1 if 2 < x…

A:

Q: The probability density of a random variable X is given in the figure below.     From this…

A:

Q: Define probability density function and obtain the relationship between probability ànd probability…

A:

Q: The variance of a discrete random variable X with probability density function P, denoted by Var[X],…

A: Given that  Variance of a discrete random with probability density functions pi , denoted by Var(X)

Q: For a continuous random variable x, what does the probability density function f(x) represents?

A: Given: For a continuous random variable x, the graph of the continuous probability distribution is a…

Q: The probability density function of the random variable X whose moment generating function (¹) ty…

A: Let us consider, the probability density function,

Q: Let X and Y be two independent random variables, and define Z = min(X, Y ) then write the cumulative…

A: Given that X and Y be two independent random variables exponentially distributed with rates λ and μ…

Q: andom variable

A: The cumulative function is given as, fxx=10.5821-x2  , -0.3≤x≤0.30      ,       O.W. The probability…

Q: Find the density function of random variable X.

A:

Q: Mean of the discrete random variable is the __ of probability mass function

A: Mean of the discrete random variable is the __ of probability mass function We have to fill the…

Q: Find the probability density function for the random variable X cumulative distribution function is…

A: Given :  Fx(x)=0 , x≤0x , 0&lt;x&lt;11 , x≥1   Let P(x) be the probability density function of X the…

Q: A random variable X has the cumulative distribution function probability density function F(x) = e*…

A: Given that, a random variable X has cdf:- F(x) = ex ,      [0, z ]

Q: The probability density function for a discrete random variable X a. Is usually normal b. Is usually…

A: The probability density function for a discrete random variable X  Explanation: The probability…

Q: Let Z be the standard normal random variable. Let X1 = Z, X2 = -Z be independent random variables.…

A: We have given that,  Z from the standard normal distribution with mean = 0 and variance = 1 i.e,…

Q: Let X be a random variable with cumulative distribution functic given by: F(x) = 1 – e-Az Find the…

A: Hello! As you have posted 2 different questions, we are answering the first question. In case you…

Q: a) X is a random variable giving time (in minutes) during which a certain electrical equipment is…

A:

Q: The probability density of a random variable X is given in the figure below.     From this…

A:

Q: Find out the skew and skewness of a uniform probability density function for a random variable X.

A:

Q: The probability density of a random variable X is given in the figure below.     From this…

A: we have to find probability.

Q: The probability density function for the continuous random variable X is: a) What is the…

A:

Q: The probability density of a random variable X is given in the figure below. 1 From this density,…

A:

Q: Let X be a random variable whose probability density function is plotted below. If one was to…

A: uniform (0,1) from the graph it is straight line  it passes through origin

Q: Define and explain joint distribution function and joint density function of two random variables X…

A:

Q: 4. Let X be a random variable with cumulative distribution function given by: F(r) = 1 – e¯Az Find…

A: 1): pdf of x :f(x)=lambda*e^-(lambda*x) X follow exponential distribution  2): expected value of x…

Q: Combined probability density function of continuous random variables X and Y -∞<x<∞ , -∞<y<∞ If it…

A:

Q: [2] X is an exponential random variable with variance 9. If (X, Y = (2, otherwise, 1<x<4 find the…

A: Introduction to exponential distribution: A random variable X is said to have a exponential…

Q: The probability density of a random variable X is given in the figure below. From this density, the…

A: Uniform distribution :  It is a probability distribution where all outcomes are equally likely.…

Q: The probability density function of X discrete random variable given in the photograph is given.…

A: The expected value of the given table is, Ex=x1fx1x1+x2fx2x2+x3fx3x3+x4fx4x4+x5fx5x5+x6fx6x6…

Q: Find the probability density function of the difference of two independent random variables, ea

A: Let us consider the two independent variables x1 and x2 from the density function, f(x)=α2xe-αx,…

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!