i=1 Consider the random walk stochastic process Sn = So + Xi, where So = 0, and the independent identically distributed (iid) X; are the modified Bernoulli random variables taking values 2 and -1 with proba- bilities p and 1-p, respectively. a. Calculate E[Sn] and Var[Sn] and variance definition or formula. using the expectation b. Derive the generating function of this random walk Gs, (s). c. Use the generating function directly to calculate E[Sn] Var[Sn] and hence re-confirm the results in question la. , and d. Sketch the plot of the discrete pdf, and discuss its relation to the normal distribution for p = 0.5
i=1 Consider the random walk stochastic process Sn = So + Xi, where So = 0, and the independent identically distributed (iid) X; are the modified Bernoulli random variables taking values 2 and -1 with proba- bilities p and 1-p, respectively. a. Calculate E[Sn] and Var[Sn] and variance definition or formula. using the expectation b. Derive the generating function of this random walk Gs, (s). c. Use the generating function directly to calculate E[Sn] Var[Sn] and hence re-confirm the results in question la. , and d. Sketch the plot of the discrete pdf, and discuss its relation to the normal distribution for p = 0.5
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.3: Special Probability Density Functions
Problem 46E
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![i=1
Consider the random walk stochastic process Sn
= So +
Xi, where So = 0, and the independent identically distributed (iid) X; are
the modified Bernoulli random variables taking values 2 and -1 with proba-
bilities p and 1-p, respectively.
a. Calculate E[Sn]
and Var[Sn]
and variance definition or formula.
using the expectation
b. Derive the generating function of this random walk Gs, (s).
c. Use the generating function directly to calculate E[Sn]
Var[Sn]
and hence re-confirm the results in question la.
, and
d. Sketch the plot of the discrete pdf, and discuss its relation to the normal
distribution for p = 0.5](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1822b493-2c18-4a65-99e5-18fca75fe15d%2F0a70786f-ab0b-4f3c-b9a6-36cec2ecf85d%2Fp6qql2m_processed.png&w=3840&q=75)
Transcribed Image Text:i=1
Consider the random walk stochastic process Sn
= So +
Xi, where So = 0, and the independent identically distributed (iid) X; are
the modified Bernoulli random variables taking values 2 and -1 with proba-
bilities p and 1-p, respectively.
a. Calculate E[Sn]
and Var[Sn]
and variance definition or formula.
using the expectation
b. Derive the generating function of this random walk Gs, (s).
c. Use the generating function directly to calculate E[Sn]
Var[Sn]
and hence re-confirm the results in question la.
, and
d. Sketch the plot of the discrete pdf, and discuss its relation to the normal
distribution for p = 0.5
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