# Question: Consider the light bulb problem Suppose we do not necessarily

Consider the light bulb problem. Suppose we do not necessarily want to wait for the light bulb to burn out before we make a decision as to which type of bulb is being tested. Therefore, a modified experiment is proposed. The light bulb to be tested will be turned on at 5 pm on Friday and will be allowed to burn all weekend. We will come back and check on it Monday morning at 8 am and at that point it will either still be lit or it will have burned out. Note that since there are a total of 63 h between the time we start and end the experiment and we will not be watching the bulb at any point in time in between, there are only two possible observations in this experiment ( the bulb burnt out ↔ { X < 63}) or ( the bulb is still lit ↔ { X < 63}).

(a) Given it is observed that the bulb burnt out over the weekend, what is the probability that the bulb was an - type bulb?

(b) Given it is observed that the bulb is still lit at the end of the weekend, what is the probability that the bulb was an type bulb?

(a) Given it is observed that the bulb burnt out over the weekend, what is the probability that the bulb was an - type bulb?

(b) Given it is observed that the bulb is still lit at the end of the weekend, what is the probability that the bulb was an type bulb?

**View Solution:**## Answer to relevant Questions

Suppose we are given samples of the CDF of a random variable. That is, we are given Fn = Fx (xn) at several points, xn Ɛ { x1, x2, x3,….xk. After examining a plot of the samples of the CDF, we determine that it appears ...A random variable has a CDF given by (a) Find Pr (X =0) and Pr (X=1). (b) Find Pr(X 1/2). (c) Find Pr(X > 1/2|X >0). A random variable X has a characteristic function, ϕX (ω). Write the characteristic function of Y= aX+ b in terms of ϕX (ω) and the constants a and b. Which of the following functions could be the characteristic function of a random variable? See Appendix E, Section 5 for definitions of these functions. (a) f a( ω) = rect( ω ). (b) f b( ω) = tri( ω). (c) f c( ω) = ...Suppose X is a Rician random variable with a PDF given by Derive an expression for E [euX2]. Note that this is not quite the moment- generating function, but it can be used in a similar way.Post your question