Question

Example 3 A survey of cars a certain stretch of highway during morning commute hours showed that 70% had only one occupant, 15% had 2, 10% had 3, 3% had 4, and 2% had 5. Let X represent the number of occupants in a randomly chosen car. 1. Find the probability mass function of X, and graph it. 2. Find the probability that the car had at least 3 occupants. 3. Find the probability that the car had at most 3 occupants. 4. Find the probability that the car had at least 2 occupants and not more than 4 occupants. 5. Determine the CDF for the Example and then plot the CDF

Answer 1

O xo represonly the no. of ocuponty in a chosen car. o Pin oxix Fly-z) XL 12131415 10.15 ply=x) 10.7 0.1 10.03 10.02 Graph of P(x-xy Pex 1 0.70 0.15 o. Lo DIO? 6.027 1 2 3 4 5 220 © Pľx 7,31 = P(x has at least 3 occupants] = P(x = 3) + P(X=4) +POX = 5) [plå73) = 0.15 pm e (3 pl x<31 - PEx had at most 3 ocupante? - plx=1) +P6X =2) +plX= 3) [PRX53] = 0.95 ans p ſ x has at least 2 occupante, and not more than 4 occupande ] - Pſ x72 and x 74] =P [X32 A x<+] - PC x= 27 +P [X =3) |p(x0,2 98 44]= 0.25 ANS. GS Scanned with CamScanner..

TL Tai C.D-F of X x 1 Fycm) 0.70 15 TY 1 2 0.95 3 0.95 4 10.98 11.60 plot of CDF F(X), t 0198 8.95 0185 F 0170 rt 1 2 3 4 5 Scanned with CamScanner