State whether the following statements are True or False and also give the reason in support of your answer.

(a) Sample space of a (i) random experiment tossing two coins simultaneously and (ii) One coin two times is the same.

(b) Standard deviation of a random variable X may take any real value, i.e. its value lies in the interval(ゆす。,

c) If events  are mutually exclusive and exhaustive then will be greater than 1/2 but less than 1.

(d) If S is sample space of a random experiment and E is an event defined on this sample space then P(SE)-1.

(e) If X is a random variable having range set (0, 1, 2, 3) then the set (xS:X(x)0 is an event having at least one outcome of the random experiment.

(a) False
The sample space for tossing two coins simultaneously is {HH, HT, TH, TT}, while the sample space for tossing one coin two times is {H, T} repeated twice, giving {HH, HT, TH, TT} as well. Though the elements appear the same, the way the sample space is constructed differs because the first involves simultaneous outcomes and the second involves sequential outcomes. So, they are _________ _____ _________ _______ _______ ______ ___ ________.
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