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All Probability

on Feb 02, 2010

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All ProbabilityPresentation Transcript

• Questions
• Question 5
• There are 2 bags. One Containing 5 white balls and 4 black ball and other containing 4 white and 5 black balls. One ball is transferred from one the first bag to the second bag then a ball is drawn from the second bag. What is the probability that is a white ball.
• 41/90
• Questions Random variable
• Questions
• Find the expected value of the heads when two coins are tossed
• Question no 2
• A box contains six tickets. Two of the tickets carry a price of Rs. 5 each and the other four prices of Re.1
• A) If one ticket is drawn what is the expected value of the price?
• B)If two tickets are drawn ,what is the expected value of the price.
• Questions Binomial Distribution
• The binomial distribution describes the behavior of a count variable X if the following conditions apply:
• 1: The number of observations n is fixed.
• 2: Each observation is independent.
• 3: Each observation represents one of two outcomes (&quot;success&quot; or &quot;failure&quot;).
• 4: The probability of &quot;success&quot; p is the same for each outcome.
• If these conditions are met, then X has a binomial distribution with parameters n and p, abbreviated B(n,p).
• A random variable X is said to follow Binomial distribution with parameters n and p if its probability function is
• f(x)= nC x p x q n-x
• Where x= 0,1,2,….n
• P + q = 1
• Mean of binomial distribution
• Mean of binomial distribution = np
• n- number of trials
• p- probability of success
• Standard deviation of a binomial distribution
• Standard deviation of a binomial distribution = npq
• n- number of trials
• p– probability of success
• q- Probability Of Failure or (1-p)
• Question no 1
• Four coins are tossed simultaneously. What is the probability of getting two heads
• Question No 2
• Eight unbiased coins are tossed simultaneously. Find the probability of getting
• Number of heads ranging from 3 to 5
• Question no 3
• Eight coins are tossed simultaneously 256 times . Find the expected frequencies
• Find mean and Standard Deviation
• Home work
• The following Data show the number of seeds germinating out of 10 on damp filter for 80 sets of seeds. Fit a binomial distribution of this data and find the expected frequencies
• Poison Distribution Called law of improbable events-describe the behaviour of rare events Discrete Probability distribution
• Formula
• The Probability of N success out of n trials is given by
• Where x is a discrete random variable assuming values 0,1,2…
• m is called parameter of Poisson distribution
• Example
• ., Find the probability of 4 customers arriving in 3 minutes when the mean is 3.6.
• Question no 1
• If 3% of electric bulbs manufactured by a company are defective. Find the probability that in a sample of 100 bulbs exactly five bulbs are defective
• Question No 2
• Fit a poison distribution to the following data and calculate the theoretical frequencies
• X 0 1 2 3 4
• Y 123 59 14 3 1
• Home Work
• Between the hours 2 and 4 pm the average number of phone calls per minute coming into the switch board of a company is 2.5. find the probability that during one particular minute there will be
• No phone call at all
• Exactly two calls
• At least Five calls
• Home work
• Find the probability that almost 5 defective fuses will be found in a box of 200 fuses. An experience shows that 2% of such fuses are defective.
• Normal distribution
• Both binomial and Poisson distributions consist of all the values (finite ) of a random variable that made up of these discrete and associated probabilities
• Normal probability distribution is one of the most frequently used distribution. IT is normally described in terms of continuous curve in the shape of a bell (symmetrical)
• Example
• The weekly wages of 1,000 workmen are normally distributed around a mean of Rs. 70 and with a standard deviation of Rs.5 Estimate the number of workers whose weekly wages will be
• Between Rs.70 and Rs.72
• Between Rs.69 and Rs.72
• More than Rs.75
• Less than Rs. 63
• Home work 1 Normal distribution
• Consider a project that yields an average cash flow of Rs. 500 lakhs with a standard deviation of Rs. 60 lakhs. Calculate the following probabilities
• Cash flow will be more than Rs. 560 lakhs
• Cash flow will be less than Rs.420 lakhs
• Cash flow will lie between Rs. 460 lakhs and Rs.540 lakhs
• Cash flow will be more than Rs. 680 lakhs