The total time, measured in units of 100 hours, that a teenager runs her hair dryer over a period of one year is a continuous random variable X that has the density function below. Use the theorem below to evaluate the mean of the random variable Y = 69X² +43X, where Y is equal to the number of kilowatt hours expended annually. Theorem: The expected value of the sum or difference of two or more functions of a random variable X is the sum or difference of the expected values of the functions, as given by the formula below. E[g(X,Y) ±h(X,Y)] = E[g(X,Y)] ± E[h(X,Y)] f(x) = X, 4 1 9 Ō 0

Q: Let Y₁,..., Yn be an iid sample from N(μ,0²), with both u and ² unknown. (a) Find the likelihood and…

A: Given that Y1, Y2...Yn be iid from N(μ, σ2) both μ,σ2 are unknownWe have to finda.. likelihood…

Q: Let X be physical distance, measured in inches, from its anchoring point where a bicycle spoke will…

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts.  In case…

Q: Given the probability density function f(x) = 1 over the interval [4, 8], find the expected value,…

A:

Q: A random variable X has the following pdf: f(x) = 9xe-3"; x > 0

A: Given: random variable x with gamma distribution with pdf  f(x)=9*x *e^-(3x)  : x>0  then to find…

Q: Find the mean, E[X], and variance, E[X2] - E[X], of a Uniform[a, b] random variable.

A: Given that X follows Uniform (a,b)  We have to find E(X) , Variance and E(X2)-E(X)

Q: Given the probability density function f (x)=1/2 over the interval [2,4] find the expected value,…

A:

Q: Given the probability density function f(x) = value, the mean, the variance and the standard…

A:

Q: Given the probability density function f(x)=1/3 over the interval [3,6] find the expected value, the…

A:

Q: Given the probability density function f(x)=14f(x)=14 over the interval [2,6][2,6], find the…

A: Given information: fx=14, 2<X<6, this is the density function of uniform distribution with a=2…

Q: ders pront, its of can be looked upon as a random variable X having the density function below, find…

A: It is given that the continuous probability distribution of random variable X with pdf isf(x) = {…

Q: The table below shows a probability density function for a discrete random variable X. What is the…

A: x P (X=x)  0 1/12 1 5/12 2 1/12 3 1/6 4 1/6 5 1/12

Q: Given the probability density function f(x)=15f(x)=15 over the interval [3,8][3,8], find the…

A: Given, f(x) = 1/5  where x ∈ 38 f(x) is a p.d.f of x follows uniform distribution  x ~ U[ 3 , 8 ]

Q: Given the probability density function f(x)=14f(x)=14 over the interval [3,7][3,7], find the…

A:

Q: The total number of hours, in units of 100 hours, that a family runs a vacuum cleaner over a period…

A: The density function of X is given as, The mean for f is,

Q: Given the probability density function f(x) = - 1 over the interval [2, 5], find the expected value,…

A: