UNIT 3
Probability
- The probability of a man hitting the target is ¼. How many times must he fire so that the probability his hitting the target at least once is greater than 2/3. [ans 3.81]
- Find the expectation of i) the sum ii) the product of the number of points on the throw of n dice. [Ans 7n/2]
- A discrete random variabl has the probability density function given below
X:-2-10123
P(X=x) : 0.2k0.12k0.12k
Find the mean, k and variance.[Ans 3/25, 6/25, 293/625]
4. A continuous random variable X has the pdf f(x) =kx2e-x. Find k, mean, variance.[Ans 1,0.5,3]
5. With usual notation find p of binomial distribution if n=6, 9P(X=4)=P(X=2) [Ans 2]
6. Find the probability that at most 4 defective bulbs will be found in box of 200 bulbs if it is known that 2 percent of the bulb are defective.
7. A manufacture knows from his expertise that the resistance from resistor he produces is normal with u=100 ohms and S.D is 2 ohms. What percentage of resistor will have resistance between 98 and 102ohms?
8. Two independent events random sample of size 8 and 10 have means 950and 100. The standard deviation of two populations is 80 and 100. Test the hypothesis that the population have the same mean. [a-1.178]
9. In a survey of 2000 boys of which 75 were intelligent, 40had educated fathers, while 85 of the unintelligent boys had uneducated fathers, do these figures support the hypothesis that educated fathers have intelligent boys.
10. A random sample of 16 deviations has mean 103.75cm. The sum of the squares of the deviation from the mean is 843.75cm.Can this sample be regarded as coming from the population having 108.75cm as the mean? [t=2.67, no]
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UNIT 3
Probability
- The probability of a man hitting the target is ¼. How many times must he fire so that the probability his hitting the target at least once is greater than 2/3. [ans 3.81]
- Find the expectation of i) the sum ii) the product of the number of points on the throw of n dice. [Ans 7n/2]
- A discrete random variabl has the probability density function given below
X:-2-10123
P(X=x) : 0.2k0.12k0.12k
Find the mean, k and variance.[Ans 3/25, 6/25, 293/625]
4. A continuous random variable X has the pdf f(x) =kx2e-x. Find k, mean, variance.[Ans 1,0.5,3]
5. With usual notation find p of binomial distribution if n=6, 9P(X=4)=P(X=2) [Ans 2]
6. Find the probability that at most 4 defective bulbs will be found in box of 200 bulbs if it is known that 2 percent of the bulb are defective.
7. A manufacture knows from his expertise that the resistance from resistor he produces is normal with u=100 ohms and S.D is 2 ohms. What percentage of resistor will have resistance between 98 and 102ohms?
8. Two independent events random sample of size 8 and 10 have means 950and 100. The standard deviation of two populations is 80 and 100. Test the hypothesis that the population have the same mean. [a-1.178]
9. In a survey of 2000 boys of which 75 were intelligent, 40had educated fathers, while 85 of the unintelligent boys had uneducated fathers, do these figures support the hypothesis that educated fathers have intelligent boys.
10. A random sample of 16 deviations has mean 103.75cm. The sum of the squares of the deviation from the mean is 843.75cm.Can this sample be regarded as coming from the population having 108.75cm as the mean? [t=2.67, no]
1
UNIT 3
Probability
- The probability of a man hitting the target is ¼. How many times must he fire so that the probability his hitting the target at least once is greater than 2/3. [ans 3.81]
- Find the expectation of i) the sum ii) the product of the number of points on the throw of n dice. [Ans 7n/2]
- A discrete random variabl has the probability density function given below
X:-2-10123
P(X=x) : 0.2k0.12k0.12k
Find the mean, k and variance.[Ans 3/25, 6/25, 293/625]
4. A continuous random variable X has the pdf f(x) =kx2e-x. Find k, mean, variance.[Ans 1,0.5,3]
5. With usual notation find p of binomial distribution if n=6, 9P(X=4)=P(X=2) [Ans 2]
6. Find the probability that at most 4 defective bulbs will be found in box of 200 bulbs if it is known that 2 percent of the bulb are defective.
7. A manufacture knows from his expertise that the resistance from resistor he produces is normal with u=100 ohms and S.D is 2 ohms. What percentage of resistor will have resistance between 98 and 102ohms?
8. Two independent events random sample of size 8 and 10 have means 950and 100. The standard deviation of two populations is 80 and 100. Test the hypothesis that the population have the same mean. [a-1.178]
9. In a survey of 2000 boys of which 75 were intelligent, 40had educated fathers, while 85 of the unintelligent boys had uneducated fathers, do these figures support the hypothesis that educated fathers have intelligent boys.
10. A random sample of 16 deviations has mean 103.75cm. The sum of the squares of the deviation from the mean is 843.75cm.Can this sample be regarded as coming from the population having 108.75cm as the mean? [t=2.67, no]
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