An ant is moving on an integer-numbered, horizontal line every second. The number ranges from −∞ to −∞. It moves to the left integer with a probability of 1/4, to the right integer with a probability of 1/2, and stays where it is with a probability of 1/4. Suppose that the ant starts at -1, 0, or 1 with equal probability at time t. Then, what is the probability the ant will be at 0 at time t + 1?
An ant is moving on an integer-numbered, horizontal line every second. The number ranges from −∞...
An ant is moving on an integer-numbered, horizontal line every second. The number ranges from −∞ to −∞. It moves to the left integer with a probability of 1/4 and to the right integer with a probability of 3/4. Suppose initially it starts at 0, what is the probability that three seconds later it will be at 1?
The motion diagram shows motion an ant moving to the right along a straight line as it is recorded every 1.0 s, starting at point at x 0.0 cm. Assuming the ant starts from rest, which graph shows ant's velocity as a function of time? t 0.0 s 8. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 15 10 O05010.0 15.0 00 50 L00 5.0 00 50 00 15.0 00 5.0 100...
02: Consider a line axis where there are blocks at positionx - 3 and x--3 and a point moves along the axis. Every time the point at position x (-3 <x <3) can either move left (x 1) with probability of 0.5 or move right (x + 1) with probability of 0.5. However, it cannot penetrate the block (e.g., at position x- 3, if the point keeps moving right, it stays in the same position. This situation still counts one...
Q2: Consider a line axis where there are blocks at position x 3 and x 3 and a point moves along the axis. Every time the point at position x (-3 <x <3) can either move left (x - 1) with probability of 0.5 or move right (x +1) with probability of 0.5. However, it cannot penetrate the block (e.g., at position x 3, if the point keeps moving right, it stays in the same position. This situation still counts...
Q2: Consider a line axis where there are blocks at position x 3 and x 3 and a point moves along the axis. Every time the point at position x (-3 <x <3) can either move left (x - 1) with probability of 0.5 or move right (x +1) with probability of 0.5. However, it cannot penetrate the block (e.g., at position x 3, if the point keeps moving right, it stays in the same position. This situation still counts...
Consider a line axis where there are blocks at position x = 3 and x = -3 and a point moves along the axis. Every time the point at position x (-3 < x < 3) can either move left (x - 1) with probability of 0.5 or move right (x + 1) with probability of 0.5. However, it cannot penetrate the block (e.g., at position x = 3, if the point keeps moving right, it stays in the same...
An ant is moving around the unit circle in the plane so that its location is given by the parametric equations (cos(π t), sin(π t)). Assume the distance units in the plane are "feet" and the time units are "seconds". In particular, the ant is initially at the point A=(1,0). A spider is located at the point S=(3,0) on the x-axis. The spider plans to move along the tangential line pictured at a constant rate. Assume the spider starts moving...
There are a number of students standing in a single file line. Each student is numbered sequentially from 0. Each student also has a binary digit associated with them, where 0 indicate the student's performance is above average and 1 indicates the student's performance is below average. The teacher wants to groupe the sudent by performance opposite ends of the line such that the number of adjacent pairs of students where one student is a 0 and the other student...
Suppose Alice is sitting at a circular table with 4 chairs
labeled {1, 2, 3, 4} and sitting initially at a random chair. Every
minute she moves to her left or right at random with equal
probability. Consider the Markov chain associated to the sequence
of her positions X0, X1, . . . .
1. Write the state space, the distribution of X0 and the
distribution of X1.
2. Write the transition matrix.
3. Assume she is at chair one...
) Draw a Markov diagram modelling the following A fly moves along a straight line in unit increments. At each time period', it moves one unit to the left with probability 0.3 ¢ to the right with probability 0.3 € stays at the same place with boobability 0.4, independently of the past history of movements. A Spideo is luoking at positions 1 & m=4, if the lands there it is captured & the process terminates. Assume that the fly starts...