1 Suppose that the expectation of a random variable X is 5. Which of the following statements is true?

• There is a sample point at which X has the value 5.
• There is a sample point at which X has value greater than 5.
• There is a sample point at which X has a value greater than or equal to 5.
• None of the above

2 The number of binary strings of n zeros and k ones that no two ones are adjacent is

• n-1 C k
• n C k
• n C k+l
• None of the above

3.Consider the regular expression (0 + 1) (0 + 1)……..n times. The minimum state finite automation that recognizes the language represented by this regular expression contains

• n states
• n + I states
• n + 2 states

(d) None of the above

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4 Context-free languages are closed under:

• Union , intersection
• Union , Kleene closure
• Intersection, complement
• Complement, Kleene Closure

5. Let L p be the set of all languages accepted by a PDA by final state and L E the set of all languages accepted by empty stack. Which of the following is true?

(a) L D = L E (b) L D É L E

(c) L D = L E (d) None of the above

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