(c) Find the mean and variance for the random variable Y, the number tained when a random digit generator is activated once. Hint: The sum of the first n positive integers is n(n + 1)/2; the sum of the squares of the first 88 INTRODUCTION TO PROBABILITY AND STATISTICS n positive integers is n(n + 1)(2n + 1)/6. 35. Let the density for X be given by f(x) = ce¯* x = 1, 2, 3, . . · Jedt nsv (a) Find the value of c that makes this a density. sD A bni a அபப்டு ians 1, 2, noinctosdrbni (b) Find the moment generating function for X. (C) Use mx(t) to find E[X]. iscrowe offwel tauisvg dTgipenib (X bni ( ug EIX quedyh Section 3.5 6. LetX be binomial with parameters n = 15 and p = .2. (a) Find the expression for the density for X. (b) Find the expression for the moment generating function for X. (c) Find E[X] and Var X. (d) Find E[X], E[X²], and Var X using the moment generating function, thus verifying your answer to part (c) of this exercise. (e) Find P[X < 1] by evaluating the density directly. Compare your answer to that given in Table I of App. A.o ai Bid (f) Draw dot diagrams similar to that of Fig. 3.2 to illustrate each of these probabilities, and find the probabilities using Table I of App. A. dehsv mdbnsT STzib A CE P[X < 5] vo P[X < 5] F(9) 3e P[2 < X < 7] P[X > 3] ndomori. F(20) sd a anininido to lbino rats used to study the hormonal regulation of a metabolic pathway a iected with a drug that inhibits body synthesis of protein. The probability th pA, obem P[2 < X < 7] P[X = 10] aidpdog rat will die from the drug before the experiment is over is .2. If 10 animals eated with the drug, how many are ted
(c) Find the mean and variance for the random variable Y, the number tained when a random digit generator is activated once. Hint: The sum of the first n positive integers is n(n + 1)/2; the sum of the squares of the first 88 INTRODUCTION TO PROBABILITY AND STATISTICS n positive integers is n(n + 1)(2n + 1)/6. 35. Let the density for X be given by f(x) = ce¯* x = 1, 2, 3, . . · Jedt nsv (a) Find the value of c that makes this a density. sD A bni a அபப்டு ians 1, 2, noinctosdrbni (b) Find the moment generating function for X. (C) Use mx(t) to find E[X]. iscrowe offwel tauisvg dTgipenib (X bni ( ug EIX quedyh Section 3.5 6. LetX be binomial with parameters n = 15 and p = .2. (a) Find the expression for the density for X. (b) Find the expression for the moment generating function for X. (c) Find E[X] and Var X. (d) Find E[X], E[X²], and Var X using the moment generating function, thus verifying your answer to part (c) of this exercise. (e) Find P[X < 1] by evaluating the density directly. Compare your answer to that given in Table I of App. A.o ai Bid (f) Draw dot diagrams similar to that of Fig. 3.2 to illustrate each of these probabilities, and find the probabilities using Table I of App. A. dehsv mdbnsT STzib A CE P[X < 5] vo P[X < 5] F(9) 3e P[2 < X < 7] P[X > 3] ndomori. F(20) sd a anininido to lbino rats used to study the hormonal regulation of a metabolic pathway a iected with a drug that inhibits body synthesis of protein. The probability th pA, obem P[2 < X < 7] P[X = 10] aidpdog rat will die from the drug before the experiment is over is .2. If 10 animals eated with the drug, how many are ted
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#36 part d please
![(c) Find the mean and variance for the random variable Y, the number
tained when a random digit generator is activated once. Hint: The sum of
the first n positive integers is n(n + 1)/2; the sum of the squares of the first
88 INTRODUCTION TO PROBABILITY AND STATISTICS
n positive integers is n(n + 1)(2n + 1)/6.
35. Let the density for X be given by
f(x) = ce¯*
x = 1, 2, 3, . . · Jedt nsv
(a) Find the value of c that makes this a density. sD A bni a
அபப்டு
ians 1, 2,
noinctosdrbni
(b) Find the moment generating function for X.
(C) Use mx(t) to find E[X].
iscrowe offwel
tauisvg dTgipenib (X bni (
ug EIX quedyh
Section 3.5
6. LetX be binomial with parameters n = 15 and p = .2.
(a) Find the expression for the density for X.
(b) Find the expression for the moment generating function for X.
(c) Find E[X] and Var X.
(d) Find E[X], E[X²], and Var X using the moment generating function, thus
verifying your answer to part (c) of this exercise.
(e) Find P[X < 1] by evaluating the density directly. Compare your answer to
that given in Table I of App. A.o ai Bid
(f) Draw dot diagrams similar to that of Fig. 3.2 to illustrate each of these
probabilities, and find the probabilities using Table I of App. A.
dehsv mdbnsT STzib A CE
P[X < 5]
vo P[X < 5] F(9)
3e P[2 < X < 7]
P[X > 3]
ndomori.
F(20)
sd a
anininido to
lbino rats used to study the hormonal regulation of a metabolic pathway a
iected with a drug that inhibits body synthesis of protein. The probability th
pA, obem
P[2 < X < 7]
P[X = 10]
aidpdog
rat will die from the drug before the experiment is over is .2. If 10 animals
eated with the drug, how many are
ted](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc074fc7e-4e48-46f1-bfc4-aee6ba4e6262%2F559c5c0d-267b-4ec4-bc0f-38a4a64b3405%2Foocpc0j.jpeg&w=3840&q=75)
Transcribed Image Text:(c) Find the mean and variance for the random variable Y, the number
tained when a random digit generator is activated once. Hint: The sum of
the first n positive integers is n(n + 1)/2; the sum of the squares of the first
88 INTRODUCTION TO PROBABILITY AND STATISTICS
n positive integers is n(n + 1)(2n + 1)/6.
35. Let the density for X be given by
f(x) = ce¯*
x = 1, 2, 3, . . · Jedt nsv
(a) Find the value of c that makes this a density. sD A bni a
அபப்டு
ians 1, 2,
noinctosdrbni
(b) Find the moment generating function for X.
(C) Use mx(t) to find E[X].
iscrowe offwel
tauisvg dTgipenib (X bni (
ug EIX quedyh
Section 3.5
6. LetX be binomial with parameters n = 15 and p = .2.
(a) Find the expression for the density for X.
(b) Find the expression for the moment generating function for X.
(c) Find E[X] and Var X.
(d) Find E[X], E[X²], and Var X using the moment generating function, thus
verifying your answer to part (c) of this exercise.
(e) Find P[X < 1] by evaluating the density directly. Compare your answer to
that given in Table I of App. A.o ai Bid
(f) Draw dot diagrams similar to that of Fig. 3.2 to illustrate each of these
probabilities, and find the probabilities using Table I of App. A.
dehsv mdbnsT STzib A CE
P[X < 5]
vo P[X < 5] F(9)
3e P[2 < X < 7]
P[X > 3]
ndomori.
F(20)
sd a
anininido to
lbino rats used to study the hormonal regulation of a metabolic pathway a
iected with a drug that inhibits body synthesis of protein. The probability th
pA, obem
P[2 < X < 7]
P[X = 10]
aidpdog
rat will die from the drug before the experiment is over is .2. If 10 animals
eated with the drug, how many are
ted
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