Discrete Mathematics
Q131.
A sender (S) transmits a signal, which can be one of the two kinds: H and L with probabilities 0.1 and 0.9 respectively, to a receiver (R) In the graph below, the weight of edge (u,v) is the probability of receiving v when u is transmitted, where u,v\in\{H,L\}. For example, the probability that the received signal is L given the transmitted signal was H, is 0.7. If the received signal is H, the probability that the transmitted signal was H (rounded to 2 decimal places) is __________.Q132.
For a given biased coin, the probability that the outcome of a toss is a head is 0.4. This coin is tossed 1,000 times. Let X denote the random variable whose value is the number of times that head appeared in these 1,000 tosses. The standard deviation of X (rounded to 2 decimal place) is ________Q133.
K4 and Q3 are graphs with the following structures Which one of the following statements is TRUE in relation to these graphs?Q134.
A bag has r red balls and b black balls. All balls are identical except for their colours. In a trial, a ball is randomly drawn from the bag, its colour is noted and the ball is placed back into the bag along with another ball of the same colour. Note that the number of balls in the bag will increase by one, after the trial. A sequence of four such trials is conducted. Which one of the following choices gives the probability of drawing a red ball in the fourth trial?Q135.
Two numbers are chosen independently and uniformly at random from the set {1, 2, ..., 13}. The probability (rounded off to 3 decimal places) that their 4-bit (unsigned) binary representations have the same most significant bit is ___________Q136.
For n\gt2, let a \in \{0,1\}^n be a non-zero vector. Suppose that x is chosen uniformly at random from \{0,1\}^n. Then, the probability that \sum_{i=1}^{n}a_ix_i is an odd number is______Q138.
For the distributions given below :Which of the following is correct for the above distributions?Q139.
Let G be the non-planar graph with the minimum possible number of edges. Then G hasQ140.
Suppose Y is distributed uniformly in the open interval (1,6). The probability that the polynomial 3x^2+6xY+3Y+6 has only real roots is (rounded off to 1 decimal place) _________.