six faces of a fair (six-faced) die are marked as 1,2,3,4,5 and 6. A success on a single toss of the die is the arrence of number "3". Let X be the number of successes in the 10 independent tosses of this die. -Xa binomial random variable? Give the corresponding parameter(s); Write down the probability mass function of X; That is the probability that there are exactly two occurrences of number "3"?

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 6E
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The six faces of a fair (six-faced) die are marked as 1,2,3,4,5 and 6. A success on a single toss of the die is the
occurrence of number "3". Let X be the number of successes in the 10 independent tosses of this die.
a) Is X a binomial random variable? Give the corresponding parameter(s);
b) Write down the probability mass function of X;
c) What is the probability that there are exactly two occurrences of number "3"?
d) Determine EX and Var(X).
Transcribed Image Text:The six faces of a fair (six-faced) die are marked as 1,2,3,4,5 and 6. A success on a single toss of the die is the occurrence of number "3". Let X be the number of successes in the 10 independent tosses of this die. a) Is X a binomial random variable? Give the corresponding parameter(s); b) Write down the probability mass function of X; c) What is the probability that there are exactly two occurrences of number "3"? d) Determine EX and Var(X).
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