1. A fair coin is tossed 10 times. What is the probability that exactly 6 heads will occur.

2. If 3% of the electric bulbs manufactured by a company are defective find the probability

that in a sample of 100 bulbs exactly 5 bulbs are defective.

3. An oil exploration firm is formed with enough capital to finance 10 explorations. The

probability of a particular exploration being successful is 0.1. Find mean and variance of

the number of successful explorations.

4. Emily hits 60% of her free throws in basketball games. She had 25 free throws in last

week's game.

a) What is the expected number and the standard deviation of Emily's hit ?

b) Suppose Emily had 7 free throws in yesterday's game.What is the probability that she

made at least 5 hits?

5. A coin is loaded so that heads has 60% chance of showing up. This coin is tossed 3 times.

a) What are the mean and the standard deviation of the number of heads that turned out?

b) What is the probability that the head turns out at least twice?

c) What is the probability that an odd number of heads turn out in 3 flips?

6. According to the 2009 current Population Survey conducted by the U.S. Census Bureau,

40% of the U.S. population 25 years old and above have completed a bachelor's degree or

more. Given a random sample of 50 people 25 years old or above, what is expected

number of people and the standard deviation of the number of people who have

completed a bachelor's degree.

7. Joe throws a fair die six times and face number 3 appeared twice. It he incredibly lucky or

unusual?

8. If the probability of being a smoker among a group of cases with lung cancer is .6, what's

the probability that in a group of 8 cases you have; (a) less than 2 smokers? (b0 More

than 5? (c) What are the expected value and variance of the number of smokers?

9. The manufacturer of the disk drives in one of the well-known brands of microcomputers

expects 2% of the disk drives to malfunction during the microcomputer's warranty

Suppose that the random variable X has p.d.f. given by

?

?

? ? ?

?

elsewhere

cx x

0,

, 0 1

f(x)

Find the

value of the constant c hence determine m so that

? ? 2 X m 1 P ? ?

2) Let X be a continuous random variable with pdf

?

?

? ? ? ?

?

elsewhere

k x

x

0,

, 0 3

f(x) 5

Find the value

of the constant k hence compute

P?1? X ? 3?

3) A continuous random variable Y has the pdf given by

?

?

? ? ? ?

?

elsewhere

k y x

0,

(1 ), 4 7

f(y)

Find

the value of the constant k hence compute

P?Y ? 5?

and

P?5 ? Y ? 6?

Accidental poisoning of children is a great concern to the Poison Control Center. From the past, 12.5% of all children reported with accidental poisoning required hospitalization. For the years 1993 through 1995 records of poisoning among children were reviewed in an effort to identify areas of improvement for safety and regulation. It was found that 892 of 7434 children in this study required hospitalization. a) Describe the sampling distribution of the sample proportion in statistical notation. b) Justify your ability to use this distribution. c) Given the previous information. what is the probability that 892 or fewer of the 7434 children needed hospitalization?Problem 5. Maximum Likelihood Estimation for Poisson Populations. Consider a random sample X1,X2, ...,Xn from a Poisson population with unknown parameter a (a > 0). (See book's section 3.6 for a Poisson refresher.) (a) Derive the maximum likelihood estimator of a. (b) The Poisson distribution has been widely used to model the distribution of counts of many types, including counts of bacteria formed in liquids. Suppose the number of Legionella bacteria (which is a bacteria often found in warm water) in a sample of 1 litre of water follows the Poisson distribution with unknown parameter a. Use (a) to calculate the maximum likelihood estimate of it based on the following bacteria counts on llitre water samples: 232 225 249 233 242 203 223 229 2245.;L 230 235 217 217 192 2. Hand calculate mean, median, mode, range, variance and standard deviation for the following distribution: X represents how many brothers and sisters do you have and ! represents frequency Itotal N -3381 (SHOW YOUR WORK / CALCULATIONS) 137 79 39 17 Madian Portion Median: Range Variance Mandard deviation English United States) Focus 462 words IsRead the introduction, then sort the following into corrosive poisons, metabolic poisons, and heavy metal poisons Drag the appropriate items to their respective bins. View Available Hint(s) Reset hydrochloric acid (HCI) nitrate ions (NO. ") mercury (Hg) cyanide (C = N ) potassium hydroxide (KOH) Corrosive poisons Metabolic poisons Heavy metal poisons