1) Let X be a continuous random variable. What is true about fX(x)fX(x)? fX(2) is a...

1) Let X be a continuous random variable. What is true about fX(x)fX(x)?
fX(2) is a probability.
fX(2) is a set.
It can only take values between 0 and 1 as input.
fX(2) is a number.

2) Let X be a continuous random variable. What is true about FX(x)FX(x)?
FX(x) is a strictly increasing function.
It decreases to zero as x→∞x→∞.
FX(2) is a probability.
FX(x) can be any real number.

Expert Solution

milcah answered 6 months ago

2. Let X be a continuous random variable with PDF ?fx(x)= cx(1 − x), 0 <...

2. Let X be a continuous random variable with PDF ?fx(x)= cx(1 − x), 0 < x < 1, 0 elsewhere. (a) Find the value of c such that fX(x) is indeed a PDF. (b) Find P(−0.5 < X < 0.3). (c) Find the median of X.

Let X be a continuous random variable with a probability density function fX (x) = 2xI...

Let X be a continuous random variable with a probability density function fX (x) = 2xI (0,1) (x) and let it be the function´ Y (x) = e −x a. Find the expression for the probability density function fY (y). b. Find the domain of the probability density function fY (y).

1. Let X be a random variable with probability density function fX given by fX(x) =...

1. Let X be a random variable with probability density function fX given by fX(x) = γαγ/ (x + α)^γ+1 , x ≥ 0, 0, x < 0, where α > 0 and γ > 0. (a) Find the cumulative distribution function (cdf) FX of X. (b) Let Y = log(X+α /α) . Find the cdf of Y and identify the distribution. (c) How could a realisation of X be generated from an R(0,1) random number generator? (d) Let Z...

The probability density function of the continuous random variable X is given by fX (x) =...

The probability density function of the continuous random variable X is given by fX (x) = kx, (0 <= x <2) = k (4-x), (2 <= x <4) = 0, (otherwise) 1) Find the value of k 2)Find the mean of m 3)Find the Dispersion σ² 4)Find the value of Cumulative distribution function FX(x)

1. Let X be a continuous random variable such that when x = 10, z =...

1. Let X be a continuous random variable such that when x = 10, z = 0.5. This z-score tells us that x = 10 is less than the mean of X. Select one: True False 2. If an economist wants to determine if there is evidence that the average household income in a community is different from $ 32,000, then a two-tailed hypothesis test should be used. Select one: True False 3. α (alpha) refers to the proportion of...

A random variable Y is a function of random variable X, where y=x^2 and fx(x)=(x+1)/2 from...

A random variable Y is a function of random variable X, where y=x^2 and fx(x)=(x+1)/2 from -1 to 1 and =0 elsewhere. Determine fy(y). In this problem, there are two x values for every y value, which means x=T^-1(y)= +y^0.5 and -y^0.5. Be sure you account for both of these. Ans: fy(y)=0.5y^-0.5

2] Let x be a continuous random variable that has a normal distribution with μ =...

2] Let x be a continuous random variable that has a normal distribution with μ = 48 and σ = 8 . Assuming n N ≤ 0.05 , find the probability that the sample mean, x ¯ , for a random sample of 16 taken from this population will be between 49.64 and 52.60 . Round your answer to four decimal places.

Let X be a continuous random variable with pdf: f(x) = ax^2 − 2ax, 0 ≤...

Let X be a continuous random variable with pdf: f(x) = ax^2 − 2ax, 0 ≤ x ≤ 2 (a) What should a be in order for this to be a legitimate p.d.f? (b) What is the distribution function (c.d.f.) for X? (c) What is Pr(0 ≤ X < 1)? Pr(X > 0.5)? Pr(X > 3)? (d) What is the 90th percentile value of this distribution? (Note: If you do this problem correctly, you will end up with a cubic...

1) Let x be a continuous random variable that follows a normal distribution with a mean...

1) Let x be a continuous random variable that follows a normal distribution with a mean of 321 and a standard deviation of 41. (a) Find the value of x > 321 so that the area under the normal curve from 321 to x is 0.2224. Round your answer to the nearest integer. The value of x is_______ (b) Find the value of x so that the area under the normal curve to the right of x is 0.3745. Round...

Let X be a continuous random variable that has a uniform distribution between 0 and 2...

Let X be a continuous random variable that has a uniform distribution between 0 and 2 and let the cumulative distribution function F(x) = 0.5x if x is between 0 and 2 and let F(x) = 0 if x is not between 0 and 2. Compute 1. the probability that X is between 1.4 and 1.8 2. the probability that X is less than 1.2 3. the probability that X is more than 0.8 4. the expected value of X...

Question