Question

Random variables \(L\) and \(T\) with joint PMF given in the table. \(P_{T,L}(t, l)\) \(t = 40\text{ sec}\) \(t = 60\text{ sec}\) \(l = 1\) \(0.15\) \(0.1\) \(l = 2\) \(0.3\) \(0.2\) \(l = 3\) \(0.15\) \(0.1\) a) Find \(P_T(t)\) and \(P_L(l)\) b) Calculate \(E[L] , E[T] ,\) \(Var(L)\) and \(Var(T)\). c) Calculate \(E[LT]\) and \(Cov(L, T)\)

          Random variables \(L\) and \(T\)
with joint PMF given in the
table.
\(P_{T,L}(t, l)\) \(t = 40\text{ sec}\) \(t = 60\text{ sec}\)
\(l = 1\) \(0.15\) \(0.1\)
\(l = 2\) \(0.3\) \(0.2\)
\(l = 3\) \(0.15\) \(0.1\)
a) Find \(P_T(t)\) and \(P_L(l)\)
b) Calculate \(E[L] , E[T] ,\) \(Var(L)\) and \(Var(T)\).
c) Calculate \(E[LT]\) and \(Cov(L, T)\)

Random variables L and T
with joint PMF given in the
table.
PT,L(t, l) t = 40 sec t = 60 sec
l = 1 0.15 0.1
l = 2 0.3 0.2
l = 3 0.15 0.1
a) Find PT(t) and PL(l)
b) Calculate E[L] , E[T] , Var(L) and Var(T).
c) Calculate E[LT] and Cov(L, T)

Added by Michael G.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Adi S

07/05/2023

Step 1

Step 1: To find Pr(t), we need to sum the probabilities for each value of L for a given t. Show more…

Show all steps

Thanks for your feedback!

Random variables L and T with joint PMF given in the table. a) Find Pr(t) and P₁(1) b) Calculate E[L], E[T], Var(L) and Var(T). c) Calculate E[LT] and Cov(L,T) PT,L(t, l) t = 40 sec t = 60sec l = 1 0.15 0.1 l = 2 0.3 0.2 l = 3 0.15 0.1