AboutAbe Mantell Expertise Hello, I am a college professor of mathematics and regularly teach all levels from elementary mathematics through differential equations, and would be happy to assist anyone with such questions!
Experience Over 15 years teaching at the college level.
Organizations belong to NCTM, NYSMATYC, AMATYC, MAA, NYSUT, AFT.
Education/Credentials B.S. in Mathematics from Rensselaer Polytechnic Institute
M.S. (and A.B.D.) in Applied Mathematics from SUNY @ Stony Brook
Question QUESTION: when tossing a unbiased ,find the probaility that
1)the first head occurs on the third trial
2)at most three trials are neccesary to observe a head .
(use geometric distribution)
solution i tried plz check 2nd part can u check .
geometric distribution i,e
g(x,p)=p.(1-p)^x-1 where x=0,12...n
1).g(3,.5)=(.5)*(.5)^2
=.125
2).in second we find g(3,.5)+g(2,.5)+g(1,.5)
.125+.25+.5=.875
QUESTION: a telephone exchange receives,on average ,five calls per minute.
find the probability that 1).in a one-minute period ,no calls are received.
2).in a two -mins period fewer than four calls are received .
3).out of separate one-minute periods,there are exactly four in which two or more calls are received.
Answer 1. P(x=0)=(e^-5)(5^0)/0!=e^-5 or about 0.006738
2. Let x=# of calls for the first minute, and y=# of calls for the second minute.
. Here are the ways x+y<4, (x,y):
. (0,0),(1,0),(0,1),(1,1),(2,0),(0,2),(2,1),(1,2),(3,0) or (0,3)
. Now just calculate each one, then add them to get the total probability.
. P(x=0)P(y=0)+P(x=1)P(y=0)+...+P(x=0)P(y=3)...which turns out to be (683/3)*(exp(-10))
. or about 0.01034
3. How many separate periods?
