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ACTIVITY I

Instruction: Answer the given problems. Identify the given, formula and solution.

1. Suppose that a random variable that a coin is tossed twice so that the sample space S = ( HH, HT, TH, TT), Let X be the number of tails that can come up. Denote the sample point and Find the probability.2. Find the probability distribution of boys and girls in families with 5 children, assuming equal probabilities for boys and girls.3. A coin is tossed three times. If X is a random variable giving the number of heads that arise, construct a table showing the probability distribution of X.4. The probability function of random variable X is given by: 2p X =1 F(x) = P X = 2 4p x = 3 0 otherwise Where p is a constant. Find (a) P( Os X 1 )Solve the following items on a clean sheet of paper. Upload a photo of your answer sheet showing your name and solution. (3 items x 10 points) 1. The weight of goats at a farm is normally distributed with a mean of 60 kg and a standard deviation of 10 kg. A truck used to transport goats can only accommodate not more than 650 kg. If 10 goats are selected at random from the population, what is the probability that the total weight exceeds the maximum weight? 2. The blood groups of 200 people are distributed as follows: 40 have type A blood, 75 have type B blood, 60 have type O blood, and 25 have type AB blood. If a person from any of the group is selected at random, what is the probability that this person has an 0 blood type? How about the AB blood type? 3. The number of accidents in a production facility has a Poisson distribution with a mean of 2.7 per month. For a given month, what is the probability that there will be more than three (3) accidents