Problem 7: [8 points] The length of time to failure (in hundred of hours) for a...
Problem 7: (8 points] The length of time to failure in hundred of hours) for a transistor is a random variable Y with c.d.f. given by Fy) -{.. 1 - exp{-yº}, if y> 0, 0, elsewhere. (a) Find the p.d.f f(y) of Y and show that it is indeed a valid p.d.f [2] (b) Find the 30th percentile of Y and interpret it [2]. (e) Find E(Y) and V(Y) [2] () Find the probability that the transistor operates for at...
Problem 7: [8 points] The length of time to failure (in hundred of hours) for a transistor is a random variable Y with c.d.f. given by F(y) {: 1 - exp{-yº}, if y20, 0, elsewhere. (a) Find the p.d.f f(y) of Y and show that it is indeed a valid p.d.f [2] (b) Find the 30th percentile of Y and interpret it [2]. (c) Find E(Y) and V(Y) [2] (d) Find the probability that the transistor operates for at least...
The length of time to failure (in hundred of hours) for a transistor is a random variable Y with c.d.f. given by F(y) = ( 1 − exp{−y 2}, if y ≥ 0, 0, elsewhere. (a) Find the p.d.f f(y) of Y and show that it is indeed a valid p.d.f [2] (b) Find the 30th percentile of Y and interpret it [2]. (c) Find E(Y ) and V (Y ) [2] (d) Find the probability that the transistor operates...
Problem 7: (8 points) The length of time to failure (in hundred of hours) for a transistor is a random variable Y with e.df. given by Fy) - 1 - exp{-1}, if y> 0 0, elsewhere. (a) Find the p.d.ff(s) of Y and show that it is indeed a valid p.d.f[2] (b) Find the 30 percentile of Y and interpret it (2) (c) Find E(Y) and V(Y) (2) (d) Find the probability that the transistor operates for at least 200...
Problem 7: (8 points) The length of time to failure (in hundred of hours) for a transistor is a random variable Y with e.df. given by Fy) - 1 - exp{-1}, if y> 0 0, elsewhere. (a) Find the p.d.ff(s) of Y and show that it is indeed a valid p.d.f[2] (b) Find the 30 percentile of Y and interpret it (2) (c) Find E(Y) and V(Y) (2) (d) Find the probability that the transistor operates for at least 200...
Problem 3: The length of time to failure (in hundreds of hours) for a transistor is a random variable X with the CDF given below: 2 F(x)lTe; x20 (a) Plot the CDF by hand. (b) Derive the pdf of this random variable. (c) Compute the P(Xs0.4) 0; x<0 (d) Compute the probability that a randomly selected transistor operates for at least 200 hours. Problem 3: The length of time to failure (in hundreds of hours) for a transistor is a...
Problem 7: [8 points) The life X (in years) of a voltage regulator of a car has pdf f(1) = 33e-($)" for a > 0. (a) Show that this is a valid p.d.f. [1] (b) Derive the c.d.f. F(x) of X [2] (c) Use your answer in (b) to find the probability that the regulator will last at least 7 years? [1] (d) Given that it has lasted at least 7 years, what is the conditional probability that it will...
Problem 7: 8 points) The life X (in years) of a voltage regulator of a car has pdf f(x) Bane (9)* for x > 0. (a) Show that this is a valid p.d.f. [1] (b) Derive the c.d.f. F(x) of X [2] (C) Use your answer in (b) to find the probability that the regulator will last at least 7 years? [1] (d) Given that it has lasted at least 7 years, what is the conditional probability that it will...
20. Problem 2: (12 points) Let X1, ..., Xn represent a random sample of size n from a Rayleigh distribution with parameter 0 and p.d.f. f(0,0) = - , (a) Sow that this is a valid p.d.f. [2] (b) Derive the c.d.f of X. [2] (c) Use the c.d.f of X to obtain the median value of X and interpret it. [2] (d) Find the maximum likelihood estimate of 0. [3] (e) You are now given a random sample of...
Problem 3: [14 points) During an 8-hour shift, the proportion of time Y that a sheet- metal stamping machine is being serviced for repairs has the following distribution: f(y) | 2(1 – y), if 0<y<1, elsewhere. 0, (a) Find the probability that the machine repair-time is between 25 minutes and 40 minutes during the 8-hour shift. [3] (b) Derive the c.d.f of Y and use it to find the 25th percentile of Y. [5] (c) Find E(Y) and E(Y2) (2,2]...