# STT311 Tma Solutions

STT311

Question: The sample space denoted by \\(\\Omega \\) is the collection or totality of all possible outcomes of a conceptual ______________

Answer: experiment

Question: The class of all events associated with a given experiment is defined to be the ________________

Answer: event space

Question: If an event B depends on occurrence of event \\(A_1\\) or \\(A_2\\), then ________

Answer: \\(P(B)=P(B\\cap A_1) + P(B\\cap A_2)\\)

Question: In general, if an event B depends on occurrence of events, \\(A_1, A_2, . . . , A_n\\) . Then________

Answer: \\(P(B)=\\sum_{i-1}^{n}P(A_i)P(\\frac{B}{A_i})\\)

Question: A probability measure P on a field of subset A of set \\(\\omega \\) is a real-valued function having domain A satisfying the property____________

Answer: \\(P (\\omega) = 1\\)

Question: A probability space, denoted by \\((\\omega, A, P)\\), if \\(P_B(A)\\) is a conditional probability measure on \\(\\omega\\), then we say that \\((\\omega, A, P)\\) is the probability space obtained by conditioning \\((\\omega, A, P)\\) by the

Answer: event B

Question: Let \\(\\left [ A_n \\right ]\\) be a sequence of independent measurable sets. If \\(\\sum_{i=1}^{\\infty }P(A_n)=\\infty \\), then

Answer: \\(P(A_i)=0\\)

Question: Let x be a random variable whose image set (S) is a continuous numbers such as an interval. Then the set \\(a\\leq x\\leq b\\) is an ___________in S

Answer: event

Question: A random variable is a function whose domain of definition is the simple space S of a random ________ and whose range is a set of real numbers.

Answer: experiment

Question: Given that probability P(a < x < b) defined as \\(P(a\\leq x\\leq b)=\\int_{a}^{b}f(x)dx\\), the function f is called the ______Probability function of X

Answer: continuous

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