6. The probability density function of (lifetime of an electronic component in years) X is x² P(-112 ) U(x) 32 fx (x) = A xexp (a) What value of A will make this a valid pdf? (b) What is the probability that it will fail within 6 years, given that normally these units tend to fail within 4 to7 years? (c) What is P[IX-3]<6]? (d) If the unit is known to fail within 6-8 years, what is the probability that it fails within 7 years. CIL II

Q: Compute the derivative f'(x) for f(x) = log(x*) sin(x³).

A: Topic - derivative

Q: Determine the value of f"" (1) when f(x) = 4ln (x+3). 1. ƒ""(1) 2. f"" (1) 3. f" (1) 4. f" (1) 5. f"…

A: f(x)=4lnx+3d dx(lnx)=1xd dx(xn)=nxn-1

Q: 45. Consider the exponential random variable X with pdf f(x) = λe-I(0,0) (r). (a) Evaluate the…

A: Given that, the exponential random variable X with pdf f(x) = λe_λx,  x&gt;0

Q: Suppose X1 and X2 are iid observations from the pdf f(x]a) = ax°-le-",x > 0, a > 0. Show that (log…

A: see the attachment.

Q: ). The Exponential probability density function (PDF) is given by: = 2 imulative density function…

A: P(X &gt; s+ t | X &gt; s ) = P(X &gt; s + t , X &gt; s)P(X &gt; s)

Q: Show that if a and b are constants, then E[aX+ b] = aE[X] + b.

A: We have to show that ,We know that for a discrete variable following properties will hold :

Q: Where are the following functions continuous? a) f(x) = (2-x)/(x3 -x) b) g(x) = log(x2 -81

A: We have to find the point of continuity of the given function.

Q: The digestion time in hours of a fixed amount of food is exponentially distributed with average 45…

A: The exponential distribution is the continuous distribution which is defined for the time between…

Q: 1.Find the derivative a. f(x) =x' In x b. f(x) = (x'+x-1)' %3D c. f(x) = 4e*- x %3D

A: Since you have posted multiple subparts we solve the first three subparts for you to get the…

Q: Show that if a random variable has an exponentialdensity with the parameter θ, the probability that…

A:

Q: 2 Compute the derivative f'(x) of the logistic sigmoi 1 f (x) : 1+ exp(-x)

A: We have to find

Q: If g(a) = a°(exin²a+eoa²a), then gʻ(a) is: atcos.

A:

Q: y = Cax+) ?x5+3 (3メ+)% (4xx+)

A:

Q: f(x) = - 3 ln(8x) f'(x) = ƒ'(3)

A: Given that  f(x)=-3ln(8x) We know that differentiation of the logarithm function if y=ln(x) then…

Q: 10. It is known that the probability of being able to log on to a computer from a re- mote terminal…

A: A thorough explanation is provided below.   Explanation:The scenario described suggests that the…

Q: If land that can be farmed L is eroding continuously at a rate of 4.5% per year because of changing…

A: “Since you have asked multiple questions (a and b are not related to each other), we will solve the…

Q: Compute the cumulative distribution function for the life time of the sensor. What is the…

A: The cumulative distribution function is defined as F(x) = P(X ≤ x)

Q: Exercise 6. Using the MGF given by Equation (24), deduce the expressions for the mean and variance…

A:

Q: (1) Let X be a continuous r.v. with the following PDF:fX(x) = 0 if x &lt; 1            4 ln(x)/x^3…

A: Step 1: Step 2: Step 3: Step 4: