We use the fact that the linear combination of independent normal random variables is also a normal random variable.
a) Mean of is and variance is
Define the standard random variable Z as
using normal table required probability we get
b) The mean of is 65 and variance is
Then
Define the standard random variable Z as
using normal table required probability we get
c) mean of is variance is
Define standard random variable z as
Then using Normal table as done above gives
d) Using part d) gives
using the same procedure we get
2. Let Xi, X2, and X represent the times necessary to perform three successive repair tasks...
(25 points) 1- Let X1,X2,and X3 represent the times necessary to perform three successive repair tasks at a certain service facility. Supposethey are independent, normal rv's with expected values μί.Peanh and variances σ.σ. and σ, respectively. a) If μι μ,-H3-60 and σ-σ-o3-15 calculate PCTOS 200) and P(150 STos b) c) 200)? Using the "l's and ơi's given in part (a), calculate both P(ss s ) and P(58 S 8 62). Using the μ's and σ's given in part (a), calculate...
Let X1, X2, and X3 represent the times necessary to perform three successive repair tasks at a certain service facility. Suppose they are independent, normal rv's with expected values μ1, μ2, and μ3 and variances σ12, σ22, and σ32, respectively. (Round your answers to four decimal places.) LetX1 X2 and X3 represent the times necessary to perform three success ve epa r tasks at a certain service facility. Suppose they are independent normal rv's with expected values μι μ2 and...
Let X1, X2, and Xz represent the times necessary to perform three successive repair tasks at a certain service facility. Suppose they are independent, normal rv's with expected values 11, 12, and ilz and variances 0,²,0,?, and 03?, respectively. (Round your answers to four decimal places.) (a) If My = Hy = Hz = 70 and 0,2 = 0,2 = 032 = 15, calculate PT, s 225) and P(180 ST, s 225). P(T. 5 225) = P(180 ST. 3225) =...
Let Xy, Xy, and X2 represent the times necessary to perform three successive repair tasks at a certain service facility. Suppose they are independent, normal rv's with expected values un, Uy, and uz and variances 0,2,0,2, and az, respectively. (Round your answers four decimal places.) (a) If uy = 4y = 4z = 50 and 0,2 = 02? = 032 = 21, calculate P(T, S 171) and P(108 ST. S 171). PIT, S 171) = 9959 P(108 ST 171) =...
1. Let X, X, and X represent the times necessary to perform successive repair tasks at a certain service facility. Suppose they are independent, normal random variables with expected values p4-14 t4-60 and ?_?? ?? 15. Consider the probability a. (10 pts. 2+ 3+2+3). Is the random variable T- X5 X2-.5x, normal? Why? Calculate its expectation and variance. DAT b. (6 pts.) Calculate the desired probability.
FR2 (4+4+4 12 points) (a) Let XI, X2, X10 be a randoin sample from N(μι,σ?) and Yi, Y2, 10 , Y 15 be a random sample from N (μ2, σ2), where all parameters are unknown. Sup- pose Σ 1 (Xi X 2 0 321 (Y-Y )2-100. obtain a 99% confidence interval for σ of having the form b, 0o) for some number b (No derivation needed). (b) 60 random points are selected from the unit interval (r:0 . We want...