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After the class students can take a bus or a metro, whichever comes first, to go Keller Hall. Let random variable T1exp(1) be the waiting time in minutes for the bus and T2exp(2) be a waiting time in minutes for the metro. Assume 1=1/5 and and 2=1/10. Let random variable Z denotes the waiting time for the students. (a) What is the CDF of Z ? Hint: Z=min(T1,T2). Compute the P(Z>t)=P(minT1,T2>t)=P(T1>t,T2>t). (b) Find the expected value of Z, i.e. E[Z] ? (c) Find E[Z2] and variance Z ? (d) Compute E[Z3+2Z2] (e) Compute E[2Z] (f) Compute E[Z3]..

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After the class students can take a bus or a metro, whichever comes first, to go Keller Hall. Let random variable T1exp(1) be the waiting time in minutes for the bus and T2exp(2) be a waiting time in minutes for the metro. Assume 1=1/5 and and 2=1/10. Let random variable Z denotes the waiting time for the students. (a) What is the CDF of Z ? Hint: Z=min(T1,T2). Compute the P(Z>t)=P(minT1,T2>t)=P(T1>t,T2>t). (b) Find the expected value of Z, i.e. E[Z] ? (c) Find E[Z2] and variance Z ? (d) Compute E[Z3+2Z2] (e) Compute E[2Z] (f) Compute E[Z3].

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  • 1. After the class students can take a bus or a metro, whichever comes first, to go Keller Hall. Let random variable T1exp(1) be the waiting time in minutes for the bus and T2exp(2) be a waiting time in minutes for the metro. Assume 1=1/5 and and 2=1/10. Let random variable Z denotes the waiting time for the students. (a) What is the CDF of Z ? Hint: Z=min(T1,T2). Compute the P(Z>t)=P(minT1,T2>t)=P(T1>t,T2>t). (b) Find the expected value of Z, i.e. E[Z] ? (c) Find E[Z2] and variance Z ? (d) Compute E[Z3+2Z2] (e) Compute E[2Z] (f) Compute E[Z3].