Homework Answers
TOPIC: Use of Central Limit Theorem to approximate Binomial to Normal distribution and to find the required probability.
LetX be a random variable that takes on values between 0 and c. (i.e P(0 X-c)-1)....
LetX be a random variable that takes on values between 0 and c. (i.e P(0 X-c)-1). Show that Var(X) . Hint: You may want to first argue that EX21S cklX), and then use this inequality to show that Var(X)-C2 1 to show that Var(x)sa*X (i- E
18. LetX and Y have joint pdf/(x, y) = eッ. 0 < x < y <...
18. LetX and Y have joint pdf/(x, y) = eッ. 0 < x < y < oo and zero otherwise. (a) Find the joint pdf of S = X + Y and T-X. (b) Find the marginal pdf of T (c) Find the marginal pdf of S.
(b) (5 points) Using CLT, approximate the probability that P(X = 18). (c) (5 points) Calculate...
(b) (5 points) Using CLT, approximate the probability that P(X =
18).
(c) (5 points) Calculate P(X = 18) exactly and compare to
part(b).
8. (15 points) Let X~Binomial(30,0.6). (a) (5 points) Using the Central Limit Theorem (CLT), approximate the probability that P(X > 20).
Question 15 Not yet answered Points out of 4.00 P Flag question Letx red blood cell...
Question 15 Not yet answered Points out of 4.00 P Flag question Letx red blood cell (RBC) count in millions per cubic millimeter of whole blood. Suppose that for healthy females, x has an approximately normal distribution with mean u 4.8 and standard deviation o- 0.3 Convert the following x interval from a laboratory test to a z interval 3.9 <x <5.4 Select one: O a. 2.00 <z 13.00 b.-3.00< 18.00 @ С. 13.00くび34.00 o d. 13.00 <18.00 o e....
Approximate the given function by a Bessel series of the given p a) f(x)-
Approximate the given function by a Bessel series of the given p a) f(x)-
Approximate the given function by a Bessel series of the given p a) f(x)-
Question 5 O out - 552 j5r lav gjar VA 1 - Vg = 600 v...
Question 5 O out - 552 j5r lav gjar VA 1 - Vg = 600 v Ta: 52-90° A for Q5, Q6 and Q7 refer to the circuit drawn on the left. LT-32.52 11 Vg $ $7.51.0 7-32.52 Q.517 marks) find VA @ 10/8v 6 2.5/45°v Tjor 516 v 10 90% y © 102-90° v
2. LetX be a continuous RV uniformly distributed over [O . Let Y-sin(X). Find the pdf...
2. LetX be a continuous RV uniformly distributed over [O . Let Y-sin(X). Find the pdf of Y
a. Use the given Taylor polynomial p, to approximate the given quantity b. Compute the absolute...
a. Use the given Taylor polynomial p, to approximate the given quantity b. Compute the absolute error in the approximation assuming the exact value is given by a calculator Approximate e-004 using f(x) = -* and p(x) = 1 -x+ a. Using the Taylor polynomialpy.c-004 (Do not round until the final answer. Then round to four decimal places as needed.) b. absolute error (Uso scientific notation. Use the multiplication symbol in the math palette as needed. Round to two decimal...
6. X is binomial with n = 500 and p =.38. Use the standard normal distribution to approximate: a. P(172 SX S216) Ans...
6. X is binomial with n = 500 and p =.38. Use the standard normal distribution to approximate: a. P(172 SX S216) Ansba b. P(x > 220) Ans 6b What allows us to use the standard normal distributi approximate binomial probabilities when n is large Ans 6c
552 = 'Ub68 b. What is the value of z if the area to the feftof...
552 = 'Ub68 b. What is the value of z if the area to the feftof z is 0.3 = X -M sind on Etalle see what matches closest! Z to hina on 13 a Z=-0.52 r from table Z =-0.52 2=0
LetX be a random variable that takes on values between 0 and c. (i.e P(0 X-c)-1). Show that Var(X) . Hint: You may want to first argue that EX21S cklX), and then use this inequality to show that Var(X)-C2 1 to show that Var(x)sa*X (i- E
18. LetX and Y have joint pdf/(x, y) = eッ. 0 < x < y < oo and zero otherwise. (a) Find the joint pdf of S = X + Y and T-X. (b) Find the marginal pdf of T (c) Find the marginal pdf of S.
(b) (5 points) Using CLT, approximate the probability that P(X =
18).
(c) (5 points) Calculate P(X = 18) exactly and compare to
part(b).
8. (15 points) Let X~Binomial(30,0.6). (a) (5 points) Using the Central Limit Theorem (CLT), approximate the probability that P(X > 20).
Question 15 Not yet answered Points out of 4.00 P Flag question Letx red blood cell (RBC) count in millions per cubic millimeter of whole blood. Suppose that for healthy females, x has an approximately normal distribution with mean u 4.8 and standard deviation o- 0.3 Convert the following x interval from a laboratory test to a z interval 3.9 <x <5.4 Select one: O a. 2.00 <z 13.00 b.-3.00< 18.00 @ С. 13.00くび34.00 o d. 13.00 <18.00 o e....
Approximate the given function by a Bessel series of the given p a) f(x)-
Approximate the given function by a Bessel series of the given p a) f(x)-
Question 5 O out - 552 j5r lav gjar VA 1 - Vg = 600 v Ta: 52-90° A for Q5, Q6 and Q7 refer to the circuit drawn on the left. LT-32.52 11 Vg $ $7.51.0 7-32.52 Q.517 marks) find VA @ 10/8v 6 2.5/45°v Tjor 516 v 10 90% y © 102-90° v
2. LetX be a continuous RV uniformly distributed over [O . Let Y-sin(X). Find the pdf of Y
a. Use the given Taylor polynomial p, to approximate the given quantity b. Compute the absolute error in the approximation assuming the exact value is given by a calculator Approximate e-004 using f(x) = -* and p(x) = 1 -x+ a. Using the Taylor polynomialpy.c-004 (Do not round until the final answer. Then round to four decimal places as needed.) b. absolute error (Uso scientific notation. Use the multiplication symbol in the math palette as needed. Round to two decimal...
6. X is binomial with n = 500 and p =.38. Use the standard normal distribution to approximate: a. P(172 SX S216) Ansba b. P(x > 220) Ans 6b What allows us to use the standard normal distributi approximate binomial probabilities when n is large Ans 6c
552 = 'Ub68 b. What is the value of z if the area to the feftof z is 0.3 = X -M sind on Etalle see what matches closest! Z to hina on 13 a Z=-0.52 r from table Z =-0.52 2=0
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