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QUESTION 6 If the probability of success in a Bernoulli trial is 0.30 the variance is A) 0.70 (B) 0.46 (C) 0.30 (D) 0.21
QUESTION 6 A random variable X 1s the number of successes in a Bernoulli experiment with #z trials each with a probability of success p and a probability of failure g. The probability distribution table of X is shown.
QUESTION 2 A binomial random variable arises from the number of successes in n independent Bernoulli trials. A context not suitable for modelling using a binomial random variable is recording the number of (A) heads when a coin is tossed 12 times. (B) left-handed people in a sample of 100 people. (C) times a player hits a target from 20 shots where each shot is independent of all other shots. (D) red marbles selected when three marbles are drawn without replacement from a bag containing four blue and five red marbles.
QUESTION 12 (3 marks) The probability that a debating team wins a debate can be modelled as a Bernoulli distribution. Given that the probability of winning a debate is 3 a) Determine the mean of this distribution. [1 mark] b) Determine the variance of this distribution. [1 mark] c¢) Determine the standard deviation of this distribution. [1 mark]
QUESTION 11 (4 marks) Two random samples (A and B) were obtained using two different Bernoulli experiments. Each Bernoulli trial in the random samples was recorded as 1 (for success) or 0 (for failure). The results are shown. In sample A for each trial the mean is 0.8 and the variance is 0.16. a) Use the sample B results to determine the mean and variance for each trial in sample B. = /2 marks/ b) Compare the variability about the means of samples A and B. [2 marks]
QUESTION 15 (4 marks) In a certain game players throw one water balloon at a target. There is a one in four chance of hitting the target. a) State the probabilities of all the possible outcomes for one throw at the target. [2 marks] b) Let H be the discrete random variable for one of the possible outcomes. Determine the mean and variance of the distribution of random variable H when 20 players throw [2 marks] a water balloon at the target.
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