Week07-Lecture (20101005)

# Df of the hypothesized distribution requires

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Unformatted text preview: associated with the underlying p.d.f. Comparing the histogram of the data with the p.d.f. of the hypothesized distribution allow us to visually check the goodness of ﬁt Plotting the p.d.f. of the hypothesized distribution requires knowledge of the underlying parameters. We will deal with the issue of parameter estimation later on. • Bar Plots = Histogram for discrete distributions 8 • Example: Interarrival Times At a Bank Suppose we collect the interarrival times of customers at a banking facility over a 90-minute period in mid-afternoon: • • Suppose that a total of 174 customers arrive over 90 minutes Arrival Rate = 174 / 90 = 1.93 customers/minute 3-2+45",1)46)*&+#",""-.,/)0-1#2) (!" '!" &!" !"#\$%#&'() %!" \$!" #!" !" !)\$" !)&" !)(" !)*" #" #)\$" #)&" #)(" #)*" \$" \$)\$" \$)&" \$)(" \$)*" %" *&+#",""-.,/)0-1#2) 9 .%/0&0')'#1*2\$"-'#1*34"56/"*/7*8"*9:;/"\$"6&)** <&"=/,*>&%'&0)\$*?'#@*.&%&,\$#\$%*ABCD* (#'" (#&" (#%" (#\$" (" !#'" !#&" !#%" !#\$" !" !#\$" !#%" !#&" !#'" (" (#\$" (#%" (#&" (#'" \$" \$#\$" \$#%" \$#&" \$#'" )" PDF of Exponential with λ = 1.93 f(x) = λe-λx for all x ≥ 0 !"#\$%&%%'(&)*+',\$-* 3-2+45",1)46)*&+#",""-.,/)0-1#2) (!" '!" &!" !"#\$%#&'() %!" \$!" What is missing? !)\$" !)&" !)(" !)*" #" #)\$" #)&" #)(" #)*" \$" \$)\$" \$)&" \$)(" \$)*" %" #!" !" 10 *&+#",""-.,/)0-1#2) Scaling Issues (!" • • If we have n data points and Δ is the bin width, then the total area underneath the histogram is nΔ The t...
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